Coverart for item
The Resource Lie groups, Daniel Bump

Lie groups, Daniel Bump

Label
Lie groups
Title
Lie groups
Statement of responsibility
Daniel Bump
Creator
Subject
Language
eng
Summary
"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 (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties. 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)."--Publisher's website
Member of
Cataloging source
MIA
http://library.link/vocab/creatorDate
1952-
http://library.link/vocab/creatorName
Bump, Daniel
Dewey number
512/.482
Illustrations
illustrations
Index
index present
LC call number
QA387
LC item number
.B76 2004
Literary form
non fiction
Nature of contents
bibliography
Series statement
Graduate texts in mathematics
Series volume
225
http://library.link/vocab/subjectName
  • Lie groups
  • Lie-groepen
  • Lie, Groupes de
  • Grupos de lie
  • Lie-Gruppe
Label
Lie groups, Daniel Bump
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages [438]-445) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
pt. I: Compact groups. Haar measure -- Schur orthogonality -- Compact operators -- The Peter-Weyl theorem -- pt. II: Lie groups 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 s1(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 -- pt. III: Topics. 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 -- The philosophy of cusp forms -- Cohomology of Grassmannians
Control code
55739480
Dimensions
24 cm
Extent
xi, 451 pages
Isbn
9780387211541
Isbn Type
(hard : alk. paper)
Lccn
2004301275
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
(OCoLC)55739480
Label
Lie groups, Daniel Bump
Publication
Bibliography note
Includes bibliographical references (pages [438]-445) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
pt. I: Compact groups. Haar measure -- Schur orthogonality -- Compact operators -- The Peter-Weyl theorem -- pt. II: Lie groups 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 s1(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 -- pt. III: Topics. 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 -- The philosophy of cusp forms -- Cohomology of Grassmannians
Control code
55739480
Dimensions
24 cm
Extent
xi, 451 pages
Isbn
9780387211541
Isbn Type
(hard : alk. paper)
Lccn
2004301275
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
(OCoLC)55739480

Library Locations

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