Fermilab Fermilab Core Computing Division

Library Home |  Ask a Librarian library@fnal.gov |  Book Catalog |  Library Journals |  Requests |  SPIRES |  Fermilab Documents |

Fermilab Library
SPIRES-BOOKS: FIND KEYWORD REPRESENTATIONS OF GROUPS *END*INIT* use /tmp/qspiwww.webspi1/5328.257 QRY 131.225.70.96 . find keyword representations of groups ( in books using www Cover
Image
Call number:9783319508535:ONLINE Show nearby items on shelf
Title:Algebra II Textbook for Students of Mathematics
Author(s): Alexey L Gorodentsev
Date:2017
Size:1 online resource (XV, 370 p. 155 illus., 2 illus. in color p.)
Contents:§1Tensor Products -- §2 Tensor Algebras -- §3 Symmetric Functions -- §4 Calculus of Arrays, Tableaux, and Diagrams -- §5 Basic Notions of Representation Theory -- §6 Representations of Finite Groups in Greater Detail -- §7
Representations of Symmetric Groups -- §8 sl_2-Modules -- §9 Categories and Functors -- §10 Extensions of Commutative Rings -- §11 Affine Algebraic Geometry -- §12 Algebraic Manifolds -- §13 Algebraic Field Extensions -- §14 Examples
of Galois Groups -- References -- Hints to Some Exercises -- Index
ISBN:9783319508535
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Algebra , Mathematics , Algebra
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:9783319475127:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators: Groups, Geometry and Applications
Author(s):
Date:2017
Size:1 online resource (VIII, 239 p. 23 illus., 11 illus. in color p.)
Contents:Pseudo-Differential Operators on the Affine Group -- Pseudo-Differential Operators on Non-Isotropic Heisenberg Groups with Multi-Dimensional Center -- Curvatures of the Heisenberg Group -- Ellipticity with Global Projection Conditions
-- Multilinear Localization Operators Associated to Quaternion Fourier Transforms -- A Time-Frequency Relationship between the Langevin Equation and the Harmonic Oscillator -- Are There Quantum Operators and Wave Functions in Standard
Probability Theory -- A Class of Non-Markovian Pseudo-Differential Operators of Lévy Type -- On the Solvability of Some Systems of Integro-Differential Equations with Anomalous Diffusion -- Visualizing Discrete Complex-Valued
Time-Frequency Representations -- The Reassigned Spectrogram of the Stockwell transform -- Continuous Multi-Wavelet Transforms for Blind Signal Separation.
ISBN:9783319475127
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Mathematics , Operator theory , Partial differential equations , Information theory , Differential geometry , Probabilities , Mathematics , Operator Theory , Partial Differential Equations , Differential Geometry , Probability Theory and Stochastic Processes , Information and Communication, Circuits
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf
Title:Quantization on Nilpotent Lie Groups
Author(s): Veronique Fischer
Date:2016
Edition:1st ed. 2016
Size:1 online resource (557 p.)
Note:10.1007/978-3-319-29558-9
Contents:Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index
ISBN:9783319295589
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Progress in Mathematics: 314
Keywords: Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2014-9789462390249:ONLINE Show nearby items on shelf
Title:Recent Progress in General Topology III [electronic resource]
Author(s): K.P Hart
J van Mill
P Simon
Date:2014
Publisher:Paris : Atlantis Press : Imprint: Atlantis Press
Size:1 online resource
Note:The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland,1992 and 2002). The boo k was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in2002. The following areas experienced signifi cant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems
Contents:Topological Homogeneity
Some Recent Progress Concerning Topology of Fractals
A biased view of topology as a tool in functional analysis
Large scale versus small scale
Descriptive aspects of Rosenthal compacta
Minimality conditions in topological groups
Set
Theoretic update on Topology
Topics in Dimension Theory
Representations of dynamical systems on Banach spaces
Generalized metrizable spaces
Permanence in Coarse Geometry
Selections and Hyperspaces
Continuum Theory
Almost disjoint families and topology
Some Topics in Geometric Topology II
Topologic
ISBN:9789462390249
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Logic, Symbolic and mathematical , Topology
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2014-9783319079684:ONLINE Show nearby items on shelf
Title:Representation Theory [electronic resource] : A Homological Algebra Point of View
Author(s): Alexander Zimmermann
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra andrepresentations of groups to block the ory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more generalalgebras, such as symmetric finite dimensional algebras over a fie ld. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their maininvariants and links between them. Group theoretical applications of these theories are given such as the structure of blocks of cyclic defect groups whenever appropriate. Overall, many methods from the representation theory ofalgebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups andalgebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use
Contents:Rings, Algebras and Modules
Modular Representations of Finite Groups
Abelian and Triangulated Categories
Morita theory
Stable Module Categories
Derived Equivalences
ISBN:9783319079684
Series:eBooks
Series:SpringerLink
Series:Algebra and Applications, 1572-5553 : v19
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf
Title:Probability on Compact Lie Groups [electronic resource]
Author(s): David Applebaum
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects
Contents:Introduction
1.Lie Groups
2.Representations, Peter
Weyl Theory and Weights
3.Analysis on Compact Lie Groups
4.Probability Measures on Compact Lie Groups
5.Convolution Semigroups of Measures
6.Deconvolution Density Estimation
Appendices
Index
Bibliography
ISBN:9783319078427
Series:eBooks
Series:SpringerLink
Series:Probability Theory and Stochastic Modelling, 2199-3130 : v70
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory)
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2014-9783319057927:ONLINE Show nearby items on shelf
Title:Principles of Harmonic Analysis [electronic resource]
Author(s): Anton Deitmar
Siegfried Echterhoff
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respectivegeneralizations to non-abelian grou ps, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelicgroups, as well as a complementary section on direct an d projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonicanalysis and for researchers seeking to apply it
Contents:1. Haar Integration
2. Banach Algebras
3. Duality for Abelian Groups
4. The Structure of LCA
Groups
5. Operators on Hilbert Spaces
6. Representations
7. Compact Groups
8. Direct Integrals
9. The Selberg Trace Formula
10. The Heisenberg Group
11. SL2(R)
12. Wavelets
13. p
adic numbers and adeles
A. Topology
B. Measure and Integration
C: Functional Analysis
ISBN:9783319057927
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Visualization
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2014-9781493909384:ONLINE Show nearby items on shelf
Title:Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics [electronic resource]
Author(s): Mahir Can
Zhenheng Li
Benjamin Steinberg
Qiang Wang
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure andrepresentation theory of reducti ve algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids fromalgebraic combinatorics v endomorphism monoids induced from vector bundles v HodgeNewton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics,while the remaining contributions are research articles containing previously unpublished result s, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and LexRenner showing that the algebraic semigroups are strongly -regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics, and the theory of algebraic groupembeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings, and alge braic combinatorics merged under the umbrella of algebraic monoids
Contents:On Algebraic Semi groups and Monoids (M. Brion)
Algebraic Semi groups are Strongly
regular (M. Brion, L. E. Renner)
Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha)
Representations of Reductive Normal Algebraic Monoids (S. Doty)
On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma)
The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang)
Algebraic Monoids and Renner Monoids (Z. Li, Z. Li, Y. Cao)
Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen)
The Endomorphisms Monoid of a
ISBN:9781493909384
Series:eBooks
Series:SpringerLink
Series:Fields Institute Communications, 1069-5265 : v71
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Topological Groups , Combinatorics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2014-9781461485353:ONLINE Show nearby items on shelf
Title:Coherent States, Wavelets, and Their Generalizations [electronic resource]
Author(s): Syed Twareque Ali
Jean-Pierre Antoine
Jean-Pierre Gazeau
Date:2014
Edition:2nd ed. 2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) andvarious generalizations o f wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherentstates, wavelets, and some of their generaliz ations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take aclassical-like view of quantum states in physics. Starting from the standar d theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are squareintegrable over a homogeneous space a further step allows one to dispense with the group context altog ether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensionalwavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups,Gazeau-Klauder coherent states,coherent states forthe relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potentialapplications, from the quantum physicallyoriented,likethe quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research forgraduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research liter
Contents:Canonical Coherent States
Positive Operator
Valued Measures and Frames
Some Group Theory
Hilbert Spaces
Square Integrable and Holomorphic Kernels
Covariant Coherent States
Coherent States from Square Integrable Representations
Some Examples and Generalizations
CS of General Semidirect Product Groups
CS of Product Groups
CS Quantizations and Probabilistic Aspects
Direct Wavelet Transforms
Multidimensional Wavelets
Wavelets Related to Other G Groups
The Discretization Problem
Frames Sampling and All That
ISBN:9781461485353
Series:eBooks
Series:SpringerLink
Series:Theoretical and Mathematical Physics, 1864-5879
Series:Physics and Astronomy (Springer-11651)
Keywords: Group theory , Quantum theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9784431542704:ONLINE Show nearby items on shelf
Title:Lie Theory and Its Applications in Physics [electronic resource] : IX International Workshop
Author(s): Vladimir Dobrev
Date:2013
Publisher:Tokyo : Springer Japan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to asystem yields in general so me notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantumgroups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples ofthese new trends are presented in this volume, based on contributions fr om the Workshop Lie Theory and Its Applications in Physics held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience ofmathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theo ry
Note:Springer eBooks
ISBN:9784431542704
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics & Statistics, 2194-1009 : v36
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Geometry
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9783642394850:ONLINE Show nearby items on shelf
Title:Algebras, Quivers and Representations [electronic resource] : The Abel Symposium 2011
Author(s): Aslak Bakke Buan
Idun Reiten
yvind Solberg
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas ofmathematics like commutati ve algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systemsand triangulated categories. In addition, it in cludes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students inalgebra, representation theory and triangulated categories
Note:Springer eBooks
Contents:C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions
L. Avramov: (Contravariant) Koszul duality for DG algebras
R. Buchweitz: The fundamental group of a morphism in a triangulated category
K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras
D. Happel: Algebras of finite global dimension
K. Igusa (with G. Todorov): Continuous Frobenius categories
D.A. Jorgensen: Triangle functors from generic hypersurfaces
Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian
H. Krause: Mo
ISBN:9783642394850
Series:e-books
Series:SpringerLink (Online service)
Series:Abel Symposia, 2193-2808 : v8
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Differentiable dynamical systems
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf
Title:Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations
Author(s): Sadri Hassani
Date:2013
Edition:2nd ed. 2013
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences.
Note:Springer eBooks
Contents:Mathematical Preliminaries
I Finite
Dimensional Vector Spaces
1 Vectors and Linear Maps
2 Algebras
3 Operator Algebra
4 Matrices
5 Spectral Decomposition
II Infinite
Dimensional Vector Spaces
6 Hilbert Spaces
7 Classical Orthogonal Polynomials
8 Fourier Analysis
III Complex Analysis
9 Complex Calculus
10 Calculus of Residues
11 Advanced Topics
IV Differential Equations
12 Separation of Variables in Spherical Coordinates
13 Second
Order Linear Differential Equations
14 Complex Analysis of SOLDEs
15 Integral Transforms and Differential Equ
ISBN:9783319011950
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics , Mathematical physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781461480242:ONLINE Show nearby items on shelf
Title:Lie Groups [electronic resource]
Author(s): Daniel Bump
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range ofmaterial to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests.This second edition has substantial new material, including improved discussions ofunderlying principles, streamlining of some pro ofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the PeterWeyl theorem, Lie algebra, conjugacy of maximal tori, the Weylgroup, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flagvarieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics tha t are treated are symmetric function theory, the representation theory of the symmetric group, FrobeniusSchur duality andGL(n)GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatoric s of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and thecohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations
Note:Springer eBooks
Contents:Part I: Compact Topological Groups
1 Haar Measure
2 Schur Orthogonality
3 Compact Operators
4 The PeterWeyl Theorem
Part II: Compact Lie Groups
5 Lie Subgroups of GL(n,C)
6 Vector Fields
7 Left
Invariant Vector Fields
8 The Exponential Map
9 Tensors and Universal Properties
10 The Universal Enveloping Algebra
11 Extension of Scalars
12 Representations of sl(2,C)
13 The Universal Cover
14 The Local Frobenius Theorem
15 Tori
16 Geodesics and Maximal Tori
17 The Weyl Integration Formula
18 The Root System
19 Examples of Root Systems
ISBN:9781461480242
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v225
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf
Title:Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday
Author(s): Alan Huckleberry
Ivan Penkov
Gregg Zuckerman
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted
Note:Springer eBooks
Contents:Preface
Real group orbits on flag manifolds
Complex connections with trivial holonomy
Indefinite harmonic theory and harmonic spinors
Twistor theory and the harmonic hull
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets
Propagation of the multiplicity
freeness property for holomorphic vector bundles
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf
Weakly harmonic Maa forms and the princi
ISBN:9781461471936
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v306
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Functional analysis
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781461464068:ONLINE Show nearby items on shelf
Title:Asymptotic Geometric Analysis [electronic resource] : Proceedings of the Fall 2010 Fields Institute Thematic Program
Author(s): Monika Ludwig
Vitali D Milman
Vladimir Pestov
Nicole Tomczak-Jaegermann
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as thedimension tends to inf inity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in theFall of 2010 continued an established traditi on of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces *Concentration of measure and isoperimetric inequalities, optimal transport ation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Randommatrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working ina wide range of mathematical sciencesin particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science
Note:Springer eBooks
Contents:Preface
The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero)
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures (D. Bartosova)
On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain)
Overgroups of the Automorphism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Woodrow)
On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman)
Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelishvili)
F
ISBN:9781461464068
Series:e-books
Series:SpringerLink (Online service)
Series:Fields Institute Communications, 1069-5265 : v68
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Discrete groups , Distribution (Probability theory)
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781461463337:ONLINE Show nearby items on shelf
Title:The Mathematics of Frobenius in Context [electronic resource] A Journey Through 18th to 20th Century Mathematics
Author(s): Thomas Hawkins
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Frobenius is best known as creator of the theory of group characters and representations, but his name is attached to a multitude of theorems and concepts from a broad spectrum of mathematical disciplines. In this book hismathematicsis presented in c ontext in two senses. The first provides the reader with the historical background necessary to understand why Frobenius undertook to solve a particular problem and to appreciate the magnitude of hisachievement. Part of the context involves Frobenius trai ning in the Berlin school of mathematics presided over by Weierstrass, Kronecker, and Kummer, from whom he learned disciplinary ideals as well as theorems. Frobeniusmathematics is also presented in context in that the author traces the ways in which his w ork was subsequently applied, developed, and ultimately incorporated into present-day mathematics. As a consequence of the contextualapproach, the reader will encounter a broad swath of diverse and important strands of 18th20th century mathematics, rangin g from the work of Lagrange and Laplace on stability of linear systems of differential equations to the theoryof complex abelian varieties. The book is divided into three parts. Part I provides an overview of Frobenius entire mathematical career and thus serves as an introduction to the main body of the book. Here, within the framework ofhis educational and professional career, his contributions to mathematics and the attendant backgrounds are briefly sketched and their subsequent impact upon the developm ent of mathematics indicated. Part II presents the development ofcore aspects of linear algebra up to and including the work of Weierstrass and Kronecker. The chapters of Part III deal in depth with Frobenius major works and can be read independently of o ne another. Thomas Hawkins was awarded theMAA Chauvenet Prize for expository writing and was the first recipient of the AMS Whiteman Prize for historical exposition. His las
Note:Springer eBooks
Contents:1. A Berlin Education
2. Professor at the Zurich Polytechnic
3. Berlin Professor
4. The Paradigm
5. Further Development of the Paradigm
6. The Problem of Pfaff
7. The Cayley
Hermite Problem and Matrix Algebra
8. Arithmetical Investigations: Linear Algebra
9. Arithmetical Investigations: Groups
10. Abelian Functions
11. Frobenius' Generalized Theory of Theta Functions
12. The Group Determinant Problem
13. Group Characters and Representations
14. Alternate Routes to Representation Theory
15. Characters and Representations after 1897
16. Loose Ends
ISBN:9781461463337
Series:e-books
Series:SpringerLink (Online service)
Series:Sources and Studies in the History of Mathematics and Physical Sciences, 2196-8810
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781461458883:ONLINE Show nearby items on shelf
Title:Drinfeld Moduli Schemes and Automorphic Forms [electronic resource] : The Theory of Elliptic Modules with Applications
Author(s): Yuval Z Flicker
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the authors original work establishing the correspondence between ell-adic rank r Galois representations andautomorphic representations of GL( r) over a function field, in the local case, and,in the global case, under a restriction at a single place. It develops Drinfelds theory of elliptic modules, their moduli schemes and coveringschemes, the simple trace formula, the fixed point formula, as w ell as the congruence relations and a simpleconverse theorem, not yet published anywhere. This version, based on a recent course taught by the author at TheOhioState University, is updated with references to research that has extended and developed the or iginal work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as avaluable resource to facilitate anentrance to this fascinating area of mathematics
Note:Springer eBooks
Contents:Elliptic Moduli
Hecke Correspondences
Trace Formulae
Higher Recipropcity Laws.
ISBN:9781461458883
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topological Groups , Number theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781461454502:ONLINE Show nearby items on shelf
Title:Lectures on Finitely Generated Solvable Groups [electronic resource]
Author(s): Katalin A Bencsath
Marianna C Bonanome
Margaret H Dean
Marcos Zyman
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Lectures on Finitely Generated Solvable Groups are based on the Topics in Group Theory course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Centerof the City University of Ne w York. While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them. The study of finitely generatedsolvable groups involves many different threads thereforethe se notes contain discussions on HNN extensions amalgamated and wreath products and other concepts from combinatorial group theory as well as commutative algebra. Alongwith Baumslags Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvablegroups. Examples are also supplied, which help illuminate many of the key concepts contained in the notes. Requiring onl y a modest initial group theory background from graduate and post-graduate students, these notes provide afield guide to the class of finitely generated solvable groups froma combinatorial group theory perspective
Note:Springer eBooks
Contents:Foreword
Preface
Preliminaries
Tools: Presentations and their Calculus
Constructions
Representations andaTheorem of Krasner and Kaloujnine
The Bieri
Strebel Theorems
Finitely Generated Metabelian Groups
An Embedding Theorem for Finitely Generated Metabelian Groups
Sketch of Proof of Lemma 1.1
Theorem 2.1 Details
Presenting an (Internal) HNN
Extension
References
ISBN:9781461454502
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Combinatorics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9781447148326:ONLINE Show nearby items on shelf
Title:Modular Representation Theory of Finite Groups [electronic resource]
Author(s): Peter Schneider
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for exampleover the fieldof complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finitegroups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as wellas Green's direct analysis of indecomposable representations. Ther e is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's workthen establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple acategory a block is by the size and structure of its so-called 'defect group'. All these concepts are made explic it for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentationis strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the read er the group theoretic approach. In particular, in the case of defect groups a detailed proof of theequivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with thesemisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwis
Note:Springer eBooks
Contents:Prerequisites in module theory
The Cartan{Brauer triangle
The Brauer character
Green's theory of indecomposable modules
Blocks
ISBN:9781447148326
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf
Title:New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number
Author(s): Garret Sobczyk
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s
Note:Springer eBooks
Contents:1 Modular Number Systems
2 Complex and Hyperbolic Numbers
3 Geometric Algebra
4 Vector Spaces and Matrices
5 Outer Product and Determinants
6 Systems of Linear Equations
7 Linear Transformations on R^n
8 Structure of a Linear Operator
9 Linear and Bilinear Forms
10 Hermitian Inner Product Spaces
11 Geometry of Moving Planes
12 Representations of the Symmetric Group
13 Calculus on m
Surfaces
14 Differential Geometry of Curves
15 Differential Geometry of k
Surfaces
16 Mappings Between Surfaces
17 Non
Euclidean and Projective Geometries
18 Lie Gr
ISBN:9780817683856
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9788847024212:ONLINE Show nearby items on shelf
Title:Groups [electronic resource] : An Introduction to Ideas and Methods of the Theory of Groups
Author(s): Antonio Mach
Date:2012
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hlders program for attacking thisproblem in the case of finite gro ups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied bothin the finite and infinite case. Permutation groups and are treated in detail their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and thecohomology theory of groups the latter with special emphasis on the extension proble m. The sections are followed by exercises hints to the solution are given, and for most of them a complete solution is provided
Note:Springer eBooks
Contents:Normal Subgroups, Conjugation and Isomorphism Theorems
Group Actions and Permutation Groups
Generators and Relations
Nilpotent Groups and Solvable Groups
Representations
Extensions and Cohomology
Solution to the exercises
ISBN:9788847024212
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9783642308055:ONLINE Show nearby items on shelf
Title:An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists [electronic resource]
Author(s): Hajime Ishimori
Tatsuo Kobayashi
Hiroshi Ohki
Hiroshi Okada
Yusuke Shimizu
Morimitsu Tanimoto
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics.While Abelian discrete sym metries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand thethree-generation flavor structure in particular. Ind eed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark andlepton masses, and mixing angles by assuming non-Abelian discrete flavor symmet ries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abeliandiscrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory - e.g. the string theory or compactification via orbifolding thereby providing a possible bridge between the underlying theoryand the corresponding low-energy sector of particle physics. This text explicitly introduces and studies the group-theoretical a spects of many concrete groups and shows how to derive conjugacy classes, characters, representations,and tensor products for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest
Note:Springer eBooks
Contents:Introduction
Basics of Finite Groups
Subgroups and Decompositions of Multiplets
Anomalies
Non
Abelian Discrete Symmetry in Quark/Lepton Flavor Models
Useful Theorems
Representations of S4 in Different Bases
Representations of A4 in Different Bases
Representations of A5 in Different Bases
Representations of T1 in Different Bases
Other Smaller Groups
References
ISBN:9783642308055
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v858
Series:Physics and Astronomy (Springer-11651)
Keywords: Group theory , Mathematical physics , Quantum theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9783642227172:ONLINE Show nearby items on shelf
Title:The Schrdinger-Virasoro Algebra [electronic resource] Mathematical structure and dynamical Schrdinger symmetries
Author(s): Jrmie Unterberger
Claude Roger
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structurethe Schrdinger-Virasoro algebra. Just as Poincar invariance or conformal (Virasoro) invarianceplay a key role in understanding , respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study ofsome models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Liealgebra touches upon topics as various as statistical physics, vertex algebras, Po isson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and thespectral theory of Schrdinger operators.
Note:Springer eBooks
Contents:Introduction
Geometric Definitions of SV
Basic Algebraic and Geometric Features
Coadjoint Representaion
Induced Representations and Verma Modules
Coinduced Representations
Vertex Representations
Cohomology, Extensions and Deformations
Action of sv on Schrdinger and Dirac Operators
Monodromy of Schrdinger Operators
Poisson Structures and Schrdinger Operators
Supersymmetric Extensions of sv
Appendix to chapter 6
Appendix to chapter 11
Index
ISBN:9783642227172
Series:e-books
Series:SpringerLink (Online service)
Series:Theoretical and Mathematical Physics, 1864-5879
Series:Physics and Astronomy (Springer-11651)
Keywords: Algebra , Topological Groups , Mathematical physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9783642154829:ONLINE Show nearby items on shelf
Title:Symmetries and Group Theory in Particle Physics [electronic resource] : An Introduction to Space-Time and Internal Symmetries
Author(s): Giovanni Costa
Gianluigi Fogli
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is anintroduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of theMinkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standardmodel of particle physics. This book, based on several courses given by th e authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge ofclassical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures
Note:Springer eBooks
Contents:Introduction to Lie Groups and their Representations
The Rotation Group
The Homogeneous Lorentz Group
The Poincare Transformation
One Particle and Two Particle States
Discrete Operations
Relativistic Equations
Unitary Symmetries
Gauge Symmetries
Rotation Matrices and Clebsch
Gordan Coeficients
Symmetric Goups and Identical Particles
Young Tableaux and Irreducible Representations ot he Unitary Groups
Solutions
Index
ISBN:9783642154829
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Physics, 0075-8450 : v823
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematical physics , Quantum theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9783034802604:ONLINE Show nearby items on shelf
Title:Representations of Finite Groups: Local Cohomology and Support [electronic resource]
Author(s): David J Benson
Srikanth Iyengar
Henning Krause
Date:2012
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas fromcommutative algebra, co homology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been DanielQuillens description of the algebraic variety co rresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods ofalgebraic geometry to obtain representation theoretic information. Thei r work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutativeHopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins classification ofthick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localiz ing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approachto address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with rin g of operators. The book serves as an introduction to this circle of ideas
Note:Springer eBooks
Contents:Preface
1 Monday
1.1 Overview
1.2 Modules over group algebras
1.3 Triangulated categories
1.4 Exercises
2 Tuesday
2.1 Perfect complexes over commutative rings
2.2 Brown representability and localization
2.3 The stable module category of a finite group
2.4 Exercises
3 Wednesday
3.1
3.2 Koszul objects and support
3.3 The homotopy category of injectives
3.4 Exercises
4 Thursday
4.1 Stratifying triangulated categories
4.2 Consequences of stratification
4.3 The Klein four group
4.4 Exercises
5 Friday
5.1 Localising subcategories of D
ISBN:9783034802604
Series:e-books
Series:SpringerLink (Online service)
Series:Oberwolfach Seminars : v43
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9781461419396:ONLINE Show nearby items on shelf
Title:Spectra of Graphs [electronic resource]
Author(s): Andries E Brouwer
Willem H Haemers
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromaticnumber and Shannon capac ity, the connection between randomness and the 'eigenvalue gap', and applications. It continues with a presentation of some new material on trees, strongly regular graphs, two-graphs, association schemes,p-ranks of configurations and similar topics. Exerc ises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, referencesat the end of the book, an author and subject index enrich the text. Spect ra of Graphs is written for researchers, teachers and students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra andeigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theo rem and eigenvalue interlacing are included
Note:Springer eBooks
Contents:Graph spectrum
Linear algebra
Eigenvalues and eigenvectors of graphs
The second largest eigenvalue
Trees
Groups and graphs
Topology
Euclidean representations
Strongly regular graphs
Regular two
graphs
Association schemes
Distance regular graphs
p
ranks
Spectral characterizations
Graphs with few eigenvalues
References
Author Index
Subject Index
ISBN:9781461419396
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9781461412311:ONLINE Show nearby items on shelf
Title:Representing Finite Groups [electronic resource] : A Semisimple Introduction
Author(s): Ambar N Sengupta
Date:2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples withdevelopment of general and pow erful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups.The text progressessystematically and the presentation is friendly and inviting. Cent ral concepts are revisited and exploredfrom multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: ASemisimple Introduction would serve as a textbook for graduate and some advanced undergraduate c ourses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A finalchapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematic s and mathematical physics will also find this book useful. A separate solutions manual is available for instructors
Note:Springer eBooks
ISBN:9781461412311
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Quantum theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9781461407768:ONLINE Show nearby items on shelf
Title:Representation Theory of Finite Groups [electronic resource] : An Introductory Approach
Author(s): Benjamin Steinberg
Date:2012
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linearalgebra, group theory, a nd very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted.Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader. The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside'spq-theorem and the dimension theorem, permutation representations, indu ced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probabilityand statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate theusefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exerci ses add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearlyshown in diagrams. This text will engage a broad readership due to the significance of representation theory in diverse branches of mathema tics, engineering, and physics, to name a few. Its primary intended use is as a one semestertextbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a ref erence to researchers in all areas of mathematics, statistics, andseveral mathematical sciences
Note:Springer eBooks
ISBN:9781461407768
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9781461407096:ONLINE Show nearby items on shelf
Title:Buildings, Finite Geometries and Groups [electronic resource] : Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010
Author(s): N.S. Narasimha Sastry
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume collects articles inspired by the Proceedings of the ICM 2010 Satellite Conference on Buildings, Finite Geometries and Groups organized at the Indian Statistical Institute, Bangalore, from August 29 31,2010. These contributors include so me of the most active researchers in areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lietheory, and more. Contributions reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective that the authors bring to their articles on currentdevelopments and major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these fields
Note:Springer eBooks
Contents:1. On Characterizing Designs By Their Codes (B. Bagchi)
2. The Geometry of Extremal Elements in a Lie Algebra (A.M. Cohen)
3. Properties of a 27
dimensional Space of Symmetric Bilinear Forms Acted on by E6 (R. Gow)
4. On the Geometry of Global Function Fields, the Riemann
Roch Theorem, and Finiteness Properties of S
arithmetic Groups (R. Gramlich)
5. Some Remarks on Two
Transitive Permutation Groups as Multiplication Groups of Quasigroups (G. Hiss, F. Lbeck)
6. Curve Complexes Versus Tits Buildings: Structures and Applications (Lizhen Ji)
7. On Isotypies Between Galois Conj
ISBN:9781461407096
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Proceedings in Mathematics, 2190-5614 : v10
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Cell aggregation Mathematics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9781447123538:ONLINE Show nearby items on shelf
Title:Mathematical Methods for Signal and Image Analysis and Representation [electronic resource]
Author(s): Luc Florack
Remco Duits
Geurt Jongbloed
Marie-Colette Lieshout
Laurie Davies
Date:2012
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living onan n-dimensional smo oth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. Incontrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed forthe sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interestedin the fundamental methodology per se. Covering many topics at the forefront of curre nt research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduatestudents and researchers in the fields of computer vision, medical imaging and visual perception
Note:Springer eBooks
Contents:A Short Introduction to Diffusion
like Methods
Adaptive Filtering using Channel Representations
3D
Coherence
Enhancing Diffusion Filtering for Matrix Fields
Structural Adaptive Smoothing: Principles and Applications in Imaging
SPD Tensors Regularization via Iwasawa Decomposition
Sparse Representation of Video Data by Adaptive Tetrahedralizations
Continuous Diffusion Wavelet Transforms and Scale Space over Euclidean Spaces and Noncommutative Lie Groups
Left Invariant Evolution Equations on Gabor Transforms
Scale Space Representations Locally Adapted to the Geometry of Ba
ISBN:9781447123538
Series:e-books
Series:SpringerLink (Online service)
Series:Computational Imaging and Vision, 1381-6446 : v41
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Computer vision
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2012-9780817648176:ONLINE Show nearby items on shelf
Title:Representation Theory, Complex Analysis, and Integral Geometry [electronic resource]
Author(s): Bernhard Krtz
Omer Offen
Eitan Sayag
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book is an outgrowth of the special term Harmonic Analysis, Representation Theory, and Integral Geometry, held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonnduring the summer of 2007. The contributions in the volume provide a window into a variety of subjects related to reductive groups: real and complex analysis on homogeneous spaces, arithmetic aspects of moment geometry, geometry offlag varieties, restriction theory of representations, modern aspects of special functions, multiple Dirichlet series, and unfolding identities in the theory of automorphic forms. Throughout the work, great emphasis was placed onmaking the articles accessible to interested newcomers to these fields and gradu ate students. Representation Theory, Complex Analysis, and Integral Geometry aims to stimulate future research in these areas. Contributors: J. Bernstein,G. Chinta, D. Ciubotaru, J. Faraut, S. Gindikin, J. Jorgenson, J. Kramer, B. Krtz, Y.A. Neretin, K. N ishiyama, O. Offen, H. Schlichtkrull, M.J. Slupinski, R.J. Stanton, B. Speh, P.E. Trapa, T.N.Venkataramana
Note:Springer eBooks
Contents:Preface
On Function Spaces on Symmetric Spaces
A Relation Involving RankinSelberg L
Functions of Cusp Forms and Maass Forms
Orthogonal Period of a Gl3(Z) Eisenstein Series
Regular Orbits of Symmetric Subgroups on Partial Flag Varieties
Helgason's Conjecture in Complex Analytical Interior
Lectures on Lie Algebras
SteinSahi Complementary Series and Their Degenerations
The Special Symplectic Structure of Binary Cubics
On the Restriction of Representations of Sl(2C) to Sl(2,R)
Asymptotics of Spherical Functions for Large Rank: An Introduction
ISBN:9780817648176
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Number theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9789400719170:ONLINE Show nearby items on shelf
Title:Wave Equations in Higher Dimensions [electronic resource]
Author(s): Shi-Hai Dong
Date:2011
Publisher:Dordrecht : Springer Netherlands
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory andRelativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the readers disposal. Acomprehensive description of quantum wave equations in highe r dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanicstextbooks and gives scientists a fresh outlook on quantum systems in all branches of phy sics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higherdimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativis tic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem andthe generalized hypervirial theorem in higher dimensions, the Schrdinger equation with position-dependent mass and the Kaluza-Klei n theory in higher dimensions are investigated. In this context, the dependence of the energy levels onthe dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography
Note:Springer eBooks
Contents:Part I (Introduction)
Part II (Theory)
2. Special orthogonal groups (Introduction Abstract groupsOrthogonal group SO(n) Tensor representations of the SO(n) \Gamma matrix groups Spinor representations of the SO(n) Concluding remarks)
3. Rotational symmetry and Schrdinger equation in N
dimensional space (Introduction Rotation operator Orbital angular momentum operators The linear momentum operatorsRadial momentum operator Spherical harmonic polynomials Schrdinger equation for a two
body system Concluding remarks)
4. Dirac equation in higher dimensions (Introduction
ISBN:9789400719170
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
Keywords: Functional equations , Quantum theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9783642217449:ONLINE Show nearby items on shelf
Title:Supersymmetry in Mathematics and Physics [electronic resource] : UCLA Los Angeles, USA 2010
Author(s): Sergio Ferrara
Rita Fioresi
V.S Varadarajan
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new developmentin geometry, and mat hematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of thevarious questions raised
Note:Springer eBooks
Contents:Introduction
Black Holes and First Order Flows in Supergravity
Representations of Super Lie Groups: Some Remarks
On Chiral Quantum Superspaces
On the Construction of Chevalley Supergroup
Indecomposable Finite
dimensional Representations of a Class o f Lie algebras and Lie Superalgebras
On the Geometry of Super Riemann Surfaces
Charge Orbits and Moduli Spaces of Black Hole Attractors
Maximal Supersymmetry
Lie Supergroups, Unitary Representations, and Invariant Cones
Geometry of Dual Pairs of Complex Supercurves
On the Superdimension of an Irreducible Representat
ISBN:9783642217449
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2027
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Geometry , Mathematical physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9783642174049:ONLINE Show nearby items on shelf
Title:Modular Invariant Theory [electronic resource]
Author(s): H.E.A. Eddy Campbell
David L Wehlau
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classicalnon-modular case, and it descri bes many open questions. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the betterunderstood non-modular setting. It details techniques f or the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of manytopics as well as a quick survey of the elements of algebraic geometry and com mutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchersan introduction to many important topics inmodern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter
Note:Springer eBooks
Contents:1 First Steps
2 Elements of Algebraic Geometry and Commutative Algebra
3 Applications of Commutative Algebra to Invariant Theory
4 Examples
5 Monomial Orderings and SAGBI Bases
6 Block Bases
7 The Cyclic Group Cp
8 Polynomial Invariant Rings
9 The Transfer
10 Invariant Rings via Localization
11 Rings of Invariants which are Hypersurfaces
12 Separating Invariants
13 Using SAGBI Bases to Compute Rings of Invariants
14 Ladders
References
Index
ISBN:9783642174049
Series:e-books
Series:SpringerLink (Online service)
Series:Encyclopaedia of Mathematical Sciences, 0938-0396 : v139
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9783642111174:ONLINE Show nearby items on shelf
Title:Harmonic Analysis and Group Representation [electronic resource]
Author(s): A. Fig Talamanca
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Lectures: A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties.- M Cowling: Unitary and uniformly bounded representations of some simple Lie groups.- M. Duflo: Construction de representations unitaires dun groupede Lie.- R. Howe: On a no tion of rank for unitary representations of the classical groups.- V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups.- R. Zimmer: Ergodic theory, group representations and rigidity.- Seminars:A. Koranyi: Some applications of Gelfand pair s in classical analysis
Note:Springer eBooks
Contents:A. Auslander, R. Tolimeri: Nilpotent groups and abelian varieties
M Cowling: Unitary and uniformly bounded representations of some simple Lie groups
M. Duflo: Construction de reprsentations unitaires dun groupe de Lie
R. Howe: On a notion of rank for unitary representations of the classical groups
A. Koranyi: Some applications of Gelfand pairs in classical analysis
V.S. Varadarajan: Eigenfunction expansions of semisimple Lie groups
R. Zimmer: Ergodic theory, group representations and rigidity
ISBN:9783642111174
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v82
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Number theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9783642110122:ONLINE Show nearby items on shelf
Title:Theory of Group Representations and Fourier Analysis [electronic resource]
Author(s): F Gherardelli
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:A. Fig Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Reprsentations des groupes linaires p-adiques.- G.W. Mackey: Infinite-dimensional grouprepresentations and their applicati ons
Note:Springer eBooks
Contents:A. Fig Talamanca: Random Fourier series on compact groups
S. Helgason: Representations of semisimple Lie groups
H. Jacquet: Reprsentations des groupes linaires p
adiques
G.W. Mackey: Infinite
dimensional group representations and their applications
ISBN:9783642110122
Series:e-books
Series:SpringerLink (Online service)
Series:C.I.M.E. Summer Schools : v53
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9781441960559:ONLINE Show nearby items on shelf
Title:Integral Geometry and Radon Transforms [electronic resource]
Author(s): Sigurdur Helgason
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:In this text, integral geometry deals with Radons problem of representing a function on a manifold in terms of its integrals over certain submanifoldshence the term the Radon transform. Examples and far-reachinggeneralizations lead to fundamental pro blems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial differential equations and group representations). For the case ofthe plane, the inversion theorem and the support theorem ha ve had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroomuse or self-study. A number of exercises point to further results with document ation. From the reviews: Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. The contents of the book isconcentrated around the duality and double fibration, which is realized through the masterful treatment of a variety of examples. The book is written by an expert, who has made fundamental contributions to the area. Boris Rubin,Louisiana State University
Note:Springer eBooks
Contents:The Radon Transformon Rn
A Duality in Integral Geometry
The Radon Transform on Two
Point Homogeneous Spaces
The X
Ray Transform on a Symmetric Space
Orbital Integrals
The Mean
Value Operator
Fourier Transforms and Distribution: A Rapid Course
Lie Transformation Groups and Differential Operators
Bibliography
Notational Conventions
Index
ISBN:9781441960559
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Integral Transforms , Global differential geometry
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9780857297167:ONLINE Show nearby items on shelf
Title:Representations of Hecke Algebras at Roots of Unity [electronic resource]
Author(s): Meinolf Geck
Nicolas Jacon
Date:2011
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest it is one that has also seen a number of breakthroughs in recent years. Inclassifying the irreduci ble representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory ofcells, the authors develop an analogue of James' (1970) characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general. Presenting a systematic and unified treatment of representations of Heckealgebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theoryof affine Hecke algebras and Cherednik algebras. The main results of this book are obtained by a n interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, thecombinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods. This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of thefield with an interest in Hecke algebras
Note:Springer eBooks
Contents:Generic IwahoriHecke algebras
KazhdanLusztig cells and cellular bases
Specialisations and decomposition maps
Hecke algebras and finite groups of Lie type
Representation theory of ArikiKoike algebras
Canonical bases in affine type A and Arikis theorem
Decomposition numbers for exceptional types
ISBN:9780857297167
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v15
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9780857291578:ONLINE Show nearby items on shelf
Title:Representations of SL2(Fq) [electronic resource]
Author(s): Cdric Bonnaf
Date:2011
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory inthe general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provide the simplicity required for a complete description of the theory, but also the richness needed forillustrating the most delicate aspects. The developm ent of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory.To this end, the author makes use of fundamental results of l-adic cohomol ogy. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, withparticular attention to the construction of quotients by various finite groups. At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. Withthe provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well asresearchers and lecturers with an interest in Deligne-Lusztig theory
Note:Springer eBooks
Contents:Part I Preliminaries
Structure of SL2(Fq)
The Geometry of the Drinfeld Curve
Part II Ordinary Characters
Harish
Chandra Induction
Deligne
Lusztig Induction
The Character Table
Part III Modular Representations
More about Characters of G and of its Sylow Subgroups
Unequal Characteristic: Generalities
Unequal Characteristic: Equivalences of Categories
Unequal Characteristic: Simple Modules, Decomposition Matrices
Equal Characteristic
Part IV Complements
Special Cases
Deligne
Lusztig Theory: an Overview
Part V Appendices
A l
Adic Cohomology
B B
ISBN:9780857291578
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications : v13
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Group theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2011-9780817647414:ONLINE Show nearby items on shelf
Title:Developments and Trends in Infinite-Dimensional Lie Theory [electronic resource]
Author(s): Karl-Hermann Neeb
Arturo Pianzola
Date:2011
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts:infinite-dimensional Lie ( super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representationtheory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and KacMoody superalgebras.The articles in Part (B) examine connections between infinite-dimension al Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, toJordan-theoretic geometries and new results on direct-limit groups. The analytic representation theor y of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods basedon heat kernels, multiplicity freeness, BanachLiePoisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Belti, W. Bertram, J. Faulkner, Ph. Gille, H. Glckner, K.-H.Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf
Note:Springer eBooks
Contents:Preface
Part A: Infinite
Dimensional Lie (Super
)Algebras
Isotopy for Extended Affine Lie Algebras and Lie Tori
Remarks on the Isotriviality of Multiloop Algebras
Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras A Survey
Tensor Representations of Classical Locally Finite Lie Algebras
Lie Algebras, Vertex Algebras, and Automorphic Forms
KacMoody Superalgebras and Integrability
Part B: Geometry of Infinite
Dimensional Lie (Transformation) Groups
Jordan Structures and Non
Associative Geometry
Direct Limits of Infinite
Dimensional L
ISBN:9780817647414
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v288
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Geometry, algebraic , Group theory , Topological Groups , Geometry
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9783642112973:ONLINE Show nearby items on shelf
Title:Biset Functors for Finite Groups [electronic resource]
Author(s): Serge Bouc
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics onbiset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted tobiset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors tolong-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting ofadvanced results in the area, with some new ideas and proofs
Note:Springer eBooks
Contents:1 Examples
Part I General properties
2 G
sets and (H,G)
bisets
3 Biset functors
4 Simple functors
Part II Biset functors on replete subcategories
5 The Burnside functor
6 Endomorphism algebras
7 The functor CRC
8 Tensor product and internal hom
Part III p
biset functors
9 Rational representations of p
groups
10 p
biset functors
11 Applications
12 The Dade group
ISBN:9783642112973
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v1990
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , K-theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9783034604369:ONLINE Show nearby items on shelf
Title:Homological Algebra of Semimodules and Semicontramodules [electronic resource] : Semi-infinite Homological Algebra of Associative Algebraic Structures
Author(s): Leonid Positselski
Date:2010
Publisher:Basel : Springer Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on thesemi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary centralcharges, and relative non-homogeneous Koszul du ality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras,contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish- Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules,introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featur ed prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra andthe theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theo ry. In particular, it will be a valuable addition to the algebraic literature available to mathematicalphysicists
Note:Springer eBooks
Contents:Preface
Introduction
0 Preliminaries and Summary
1 Semialgebras and Semitensor Product
2 Derived Functor SemiTor
3 Semicontramodules and Semihomomorphisms
4 Derived Functor SemiExt
5 Comodule
Contramodule Correspondence
6 Semimodule
Semicontramodule Correspondence
7 Functoriality in the Coring
8 Functoriality in the Semialgebra
9 Closed Model Category Structures
10 A Construction of Semialgebras
11 Relative Nonhomogeneous Koszul Duality
Appendix A Contramodules over Coalgebras over Fields
Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Se
ISBN:9783034604369
Series:e-books
Series:SpringerLink (Online service)
Series:Monografie Matematyczne : v70
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis , Global differential geometry
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9783034604222:ONLINE Show nearby items on shelf
Title:Visions in Mathematics [electronic resource] : GAFA 2000 Special Volume, Part I
Author(s): N Alon
J Bourgain
A Connes
M Gromov
V Milman
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Visions in Mathematics - Towards 2000 was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematiciansworldwide. The goals of the conf erence were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims ofthe conference are reflected in the present set of sur vey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the first part of a two-volume set that will serve anyresearch mathematician or advanced student as an overview and guideline thro ugh the multifaceted body of mathematical research in the present and near future
Note:Springer eBooks
Contents:Foreword
Program of the Conference
Gauss
Manin determinant connections and periods of irregular connections
Problems in Hamiltonian PDE's
On a classical limit of quantum theory and the non
linear Hartree equation
Rough structure and classification
Spaces and questions
Classification of infinite
dimensional simple groups of supersymmetries and quantum field theory
Geometrization in representation theory
Geometric and unipotent crystals
y
functions of representations and lifting (Appendix by V. Vologodsky)
PDE as a unified subject
Lessons for turbulence
The
ISBN:9783034604222
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9781441908988:ONLINE Show nearby items on shelf
Title:Operational Spacetime [electronic resource] : Interactions and Particles
Author(s): Heinrich Saller
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Operational Spacetime: Interactions and Particles provides readers with a basic understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for theparametrization of op eration Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physicalproperties are related eigenvalues or invarian ts. As an explicit example, an operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge-isospin group in the general lineargroup in two complex dimensions, i.e., the Lorentz cover group, extend ed by the causal (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically,with the properties of interactions and particles as arising in the representations of its tan gent Minkowski spaces. Heinrich Saller is the author of Operational Quantum Theory I: Nonrelativistic Structures (Springer, 2006) andOperational Quantum Theory II: Relativistic Structures (Springer, 2006)
Note:Springer eBooks
Contents:Introduction and Orientation
Einstein's Gravity
Riemannian Manifolds
Mass Points
Quantum Mechanics
Quantum Fields of Flat Spacetime
External and Internal Operations
Relativities and Homogeneous Spaces
Representation Coefficients
Convolutions and Product Representations
Interactions and Kernels
Electroweak Spacetime
Masses and Coupling Constants
ISBN:9781441908988
Series:e-books
Series:SpringerLink (Online service)
Series:Fundamental Theories of Physics : v163
Series:Physics and Astronomy (Springer-11651)
Keywords: Quantum theory , Mathematical physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9780817649845:ONLINE Show nearby items on shelf
Title:Spinors in Four-Dimensional Spaces [electronic resource]
Author(s): Gerardo F Torres del Castillo
Date:2010
Edition:1
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensionalspaces with any signatu re. Some of the useful applications of four-dimensional spinors, such as YangMills theory, are derived in detail using illustrative examples. Key topics and features: Uniform treatment of the spinorformalism for four-dimensional spaces of any signature, not only the usual signature (+ + + ) employed in relativity Examples taken from Riemannian geometry and special or general relativity are discussed in detail, emphasizingthe usefulness of the two-component spinor formalism Exercises in each chapter Th e relationship of Clifford algebras and Dirac four-component spinors is established Applications of the two-component formalism, focusingmainly on general relativity, are presented in the context of actual computations Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applicationsof the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tens or. This systematic and self-contained book is suitable as a seminar text, a reference book, anda self-study guide. Reviews from the author's previous book, 3-D Spinors, Spin-Weighted Functions and their Applications: In summarythe book gathers much of wh at can be done with 3-D spinors in an easy-to-read, self-contained formdesigned for applications that will supplement many available spinor treatments. The bookshould be appealing to graduate students and researchers in relativity and mathematical physics . Mathematical Reviews The present bookprovides an easy-to-read and unconventional presentation of the spinor formalism for three-dimensional spaces with a definite or inde
Note:Springer eBooks
Contents:1 Spinor Algebra
1.1 Orthogonal Groups
1.2 Null Tetrads and the Spinor Equivalent of a Tensor
1.3 Spinorial Representation of the Orthogonal Transformations
1.3.1 Euclidean Signature
1.3.2 Lorentzian Signature
1.3.3 Ultrahyperbolic Signature
1.4 Reflections
1.5 Clifford Algebra. Dirac Spinors
1.6 Inner Products. Mate of a Spinor
1.7 Principal Spinors. Algebraic Classification
Exercises
2 Connection and Curvature
2.1 Covariant Differentiation
2.2 Curvature
2.2.1 Curvature Spinors
2.2.2 Algebraic Classification of the Conformal Curvature
2.3 Conformal Rescalings
2.4 Killing
ISBN:9780817649845
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematical Physics : v59
Series:Physics and Astronomy (Springer-11651)
Keywords: Mathematics , Topological Groups , Mathematical physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9780817649388:ONLINE Show nearby items on shelf
Title:Representation Theory and Complex Geometry [electronic resource]
Author(s): Neil Chriss
Victor Ginzburg
Date:2010
Edition:1st
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since thediscovery of D-module s in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Liegroups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. The book is largelyself-contained. . . . There is a nice introduction to symplectic geometry and a cha rming exposition of equivariant K-theory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey someinformal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it hasalready proved successful in introducing a new generation to the subject. --- Bulletin of the American Mathematical Society Th e authors have tried to help readers by adopting an informal and easily accessible style. . . . The book willprovide a guide to those who wish to penetrate into subject-matter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of oneof the chapters of the book. --- Mededelingen van het Wiskundig Genootschap Represents an important and very interesting addition to the literature. --- Mathematical R eviews
Note:Springer eBooks
Contents:Preface
Chapter 0. Introduction
Chapter 1. Symplectic Geometry
Chapter 2. Mosaic
Chapter 3. Complex Semisimple Groups
Chapter 4. Springer Theory
Chapter 5. Equivariant K
Theory
Chapter 6. Flag Varieties, K
Theory, and Harmonic Polynomials
Chapter 7. Hecke Algebras and K
Theory
Chapter 8. Representations of Convolution Algebras
Bibliography
ISBN:9780817649388
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Cell aggregation Mathematics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9780817649326:ONLINE Show nearby items on shelf
Title:Topics in Operator Semigroups [electronic resource]
Author(s): Shmuel Kantorovitz
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The theory of operator semigroups was essentially discovered in the early 1930s. Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics suchas Markov processes, th e abstract Cauchy problem, evolution equations, and mathematical physics. This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectraltheory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications. Topics include: * TheHilleYosida and LumerPhillips characterizations of semigroup generators * Th e TrotterKato approximation theorem * Katos unified treatment of the exponential formula and the Trotter product formula * The HillePhillipsperturbation theorem, and Stones representation of unitary semigroups * Generalizations of spectral theorys connect ion to operator semigroups * A natural generalization of Stones spectral integral representation to a Banachspace setting With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operatorsemigroups
Note:Springer eBooks
Contents:General Theory
Basic Theory
The Semi
Simplicity Space for Groups
Analyticity
The Semigroup as a Function of its Generator
Large Parameter
Boundary Values
Pre
Semigroups
Integral Representations
The Semi
Simplicity Space
The LaplaceStieltjes Space
Families of Unbounded Symmetric Operators
A Taste of Applications
Analytic Families of Evolution Systems
Similarity
ISBN:9780817649326
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v281
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Operator theory
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9780817648756:ONLINE Show nearby items on shelf
Title:Symmetry and Spaces [electronic resource] : In Honor of Gerry Schwarz
Author(s): H. E. A Campbell
Aloysius G Helminck
Hanspeter Kraft
David Wehlau
Date:2010
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:A group of Gerry Schwarzs colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the widerange of mathematics to which Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts,with a particular focus on characteristic 0 and mo dular invariant theory. Contributors: M. Brion A. Broer D. Daigle J. Elmer P. Fleischmann G. Freudenberg D. Greb P. Heinzner A. Helminck B. Kostant H. Kraft R. J. Shank W. Traves N. R.Wallach D. Wehlau
Note:Springer eBooks
Contents:Some Basic Results on Actions of Nonaffine Algebraic Groups
On ChevalleyShephardTodds Theorem in Positive Characteristic
Families of Affine Fibrations
On the Depth of Modular Invariant Rings for the Groups
Khlerian Reduction in Steps
On Orbit Decompositions for Symmetric
Varieties
Root Systems for Levi Factors and Borelde Siebenthal Theory
Polarizations and Nullcone of Representations of Reductive Groups
Decomposing Symmetric Powers of Certain Modular Representations of Cyclic Groups
Differential Operators on Grassmann Varieties
ISBN:9780817648756
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v278
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Field theory (Physics)
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9780817646974:ONLINE Show nearby items on shelf
Title:Representation Theory of Algebraic Groups and Quantum Groups [electronic resource]
Author(s): Akihiko Gyoja
Hiraku Nakajima
Ken-ichi Shinoda
Toshiaki Shoji
Toshiyuki Tanisaki
Date:2010
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras,representations of affine Hecke algebras, modular or ordinary representations of finite reductive groups, and representations of complex reflection groups and associated Hecke algebras. Representation Theory of Algebraic Groups andQuantum Groups is intended for graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics. Contributors: H. H. Andersen, S. Ariki, C. Bonnaf, J. Chuang, J. Du, M.Finkelberg, Q. Fu, M. Geck, V. Ginzburg, A. Hida, L. Iancu, N. Jacon, T. La m, G.I. Lehrer, G. Lusztig, H. Miyachi, S. Naito, H. Nakajima, T. Nakashima, D. Sagaki, Y. Saito, M. Shiota, J. Xiao, F. Xu, R. B. Zhang
Note:Springer eBooks
ISBN:9780817646974
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v284
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory , Algebra , Topological Groups , Number theory , Mathematical physics
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Cover
Image
Call number:SPRINGER-2010-9780387788661:ONLINE Show nearby items on shelf
Title:Groups and Symmetries [electronic resource] : From Finite Groups to Lie Groups
Author(s): Yvette Kosmann-Schwarzbach
Date:2010
Edition:First
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume. Key Topics: Brisk review of the basicdefinitions of group theory, wi th examples Representation theory of finite groups: character theory Representations of compact groups using the Haar measure Lie algebras and linear Lie groups Detailed study of SO(3) andSU(2), and their representations Spherical harmonics Represen tations of SU(3), roots and weights, with quark theory as a consequence of the mathematical properties of this symmetry group This book is illustrated with portraitsand a few historical remarks. With only linear algebra and calculus as prerequisites, Grou ps and Symmetries: From Finite Groups to Lie Groups is accessible to advanced undergraduates in mathematics and physics, and will still be ofinterest to beginning graduate students. Exercises for each chapter and a collection of problems with complete sol utions make this an ideal text for the classroom and for independent study
Note:Springer eBooks
Contents:Introduction
Acknowledgments
General Facts about Groups
Representations of Finite Groups
Representations of Compact Groups
Lie Groups and Lie Algebras
Lie groups SU(2) and SO(3)
Representations of SU(2) and SO(3)
Spherical Harmonics
Representations of SU(3) and Quarks
Problems and Solutions
Bibliography
Index
ISBN:9780387788661
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Quantum theory , Crystallography
Availability:Click here to see Library holdings or inquire at Circ Desk (x3401)
Click to reserve this book Be sure to include your ID please.
More info:Amazon.com
More info: Barnes and Noble
Full Text:Click here
Location: ONLINE

Return to the Fermilab Library catalog