Lie Groups
Published on 10. October 2011
Book
Paperback/Softback
XI, 454 pages
978-1-4419-1937-3 (ISBN)
Description
This book proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and offers a carefully chosen range of material designed to give readers the bigger picture. It explores compact Lie groups through a number of proofs and culminates in a "topics" section that takes the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as unifying them.
Reviews / Votes
From the reviews: "This book is a nice and rich introduction to the beautiful theory of Lie groups and its connection to many other areas of mathematics." (Karl-Hermann Neeb, Mathematical Reviews, 2005f) "As Lie theory prerequisites can pose a great hurdle to number-theory students attracted to this program, Bump's book will find an enthusiastic clientele even in an already crowded market. It will particularly delight readers who already know some of this material: the many short chapters generally begin with a map of the precise regress necessary to start wherever one ought. Summing Up: Highly recommended." (D.V. Feldman, CHOICE, Vol. 42 (8), April, 2005) "This book is intended for a one-year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups ... and provides a carefully chosen range of material to give the student the bigger picture." (L'Enseignement Mathematique, Vol. 50 (3-4), 2004) "This book aims to be a course in Lie groups that can be covered in one year with a group of seasoned graduate students. ... offers a wealth of complementary, partly quite recent material that is not found in any other textbook on Lie groups. ... this book covers an unusually wide spectrum of topics ... . the entire presentation is utmost thorough, comprehensive, lucid and absolutely user-friendly. ... All together, this graduate text his a highly interesting, valuable and welcome addition ... . (Werner Kleinert, Zentralblatt MATH, Vol. 1053, 2005) "Reductive Lie groups and their representations form a very broad field. The aim of the book is to select essential topics for a year course for graduate students ... . The book is nicely written and efficiently organized. ... The presented book brings a beautiful selection of a number of further important additional topics, which are worth to include into a course. It is a very important addition to existing literature on the subject." (EMS Newsletter, June, 2005) "This book gives an introduction on the graduate level to the subject of Lie groups, Lie algebras and their representation theory. The presentation is well organized and clear ... . this book is a very interesting and valuable addition to the list of already existing books on Lie groups." (J. Mahnkopf, Monatshefte fur Mathematik, Vol. 147 (3), 2006)More details
Series
Edition
2004
Language
English
Place of publication
NY
United States
Target group
Professional and scholarly
Research
Product notice
Paperback (trade)
Illustrations
1
32 s/w Abbildungen, 1 s/w Tabelle
32 black & white illustrations, 1 black & white tables
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 23 mm
Weight
702 gr
ISBN-13
978-1-4419-1937-3 (9781441919373)
DOI
10.1007/978-1-4757-4094-3
Schweitzer Classification
Other editions
Additional editions
Person
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).
Content
* Preface * Part I: Compact Groups: Haar Measure * Schur Orthogonality * Compact Operators * The Peter-Weyl Theorem * Part II: Lie Group Fundamentals: Lie Subgroups of GL(n, C) * Vector Fields * Left Invariant Vector Fields * The Exponential Map * Tensors and Universal Properties * The Universal Enveloping Algebra * Extension of Scalars * Representations of sl(2, C) * The Universal Cover * The Local Frobenius Theorem * Tori * Geodesics and Maximal Tori * Topological proof of Cartan's Theorem * The Weyl Integration Formula * The Root System * Examples of Root Systems * Abstract Weyl Groups * The Fundamental Group * Semisimple Compact Groups * Highest Weight Vectors * The Weyl Character Formula * Spin * Complexification * Coxeter Groups * The Iwasawa Decomposition * The Bruhat Decomposition * Symmetric Spaces * Relative Root Systems.* Embeddings of Lie Groups * Part III: Frobenius-Schur Duality: Mackey Theory * Characters of GL(n, C) * Duality between Sk and GL(n, C) * The Jacobi-Trudi Identity * Schur Polynomials and GL(n, C) * Schur Polynomials and Sk * Random Matrix Theory * Minors of Toeplitz Matrices * Branching Formulae and Tableaux * The Cauchy Identity * Unitary branching rules * The Involution Model for Sk * Some Symmetric Algebras * Gelfand Pairs * Hecke Algebras * Cohomology of Grassmannians * References