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Author:   Daniel Bump
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 2nd ed. 2013
Volume:   225
Dimensions:   Width: 15.50cm , Height: 2.90cm , Length: 23.50cm
Weight:   8.482kg
ISBN:  

9781493938421

ISBN 10:   1493938428
Pages:   551
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Part I: Compact Topological Groups.- 1 Haar Measure.- 2 Schur Orthogonality.- 3 Compact Operators.- 4 The Peter–Weyl 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.- 20 Abstract Weyl Groups.- 21 Highest Weight Vectors.- 22 The Weyl Character Formula.- 23 The Fundamental Group.- Part III: Noncompact Lie Groups.- 24 Complexification.- 25 Coxeter Groups.- 26 The Borel Subgroup.- 27 The Bruhat Decomposition.- 28 Symmetric Spaces.- 29 Relative Root Systems.- 30 Embeddings of Lie Groups.- 31 Spin.- Part IV: Duality and Other Topics.- 32 Mackey Theory.- 33 Characters of GL(n,C).- 34 Duality between Sk and GL(n,C).- 35 The Jacobi–Trudi Identity.- 36 Schur Polynomials and GL(n,C).- 37 Schur Polynomials and Sk.- 38 The Cauchy Identity.- 39 Random Matrix Theory.- 40 Symmetric Group Branching Rules and Tableaux.- 41 Unitary Branching Rules and Tableaux.- 42 Minors of Toeplitz Matrices.- 43 The Involution Model for Sk.- 44 Some Symmetric Alegras.- 45 Gelfand Pairs.- 46 Hecke Algebras.- 47 The Philosophy of Cusp Forms.- 48 Cohomology of Grassmannians.- Appendix: Sage.- References.- Index.

Reviews

From the reviews of the second edition: This is a graduate math level text. Concise with lots of proofs. The chapters are short enough to read in one sitting. ... I was asked to look for books on this topic. It was challenging to search for material with this title. This was the best book that I could find. I look forward to exploring this topic further. (Mary Anne, Cats and Dogs with Data, maryannedata.com, April, 2014) The book begins with a detailed explanation of the basic facts. ... It contains a discussion of very nontrivial modern applications of Lie group theory in other areas of mathematics. ... The text is very interesting and is superior to other textbooks on Lie group theory. (Dmitri Artamonov, zbMATH, Vol. 1279, 2014) This second edition of a successful graduate textbook and reference is now divided in four parts. ... the book under review is the one every one of us must have on its desk or night table. ... this is a well-organized book with clear and well-established goals, taking the interested reader to the frontiers of today's research. (Felipe Zaldivar, MAA Reviews, December, 2013)

Author Information

Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include Automorphic Forms and Representations (Cambridge University Press 1997) and Algebraic Geometry (World Scientific 1998).

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