The Resource Lie Groups, by Daniel Bump, (electronic resource)

Lie Groups, by Daniel Bump, (electronic resource)

Label
Lie Groups
Title
Lie Groups
Statement of responsibility
by Daniel Bump
Creator
Subject
Genre
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)
Member of
Cataloging source
AU@
http://library.link/vocab/creatorName
Bump, Daniel
Dewey number
  • 512.55
  • 512.482
Index
no index present
LC call number
  • QA252.3
  • QA387
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Graduate Texts in Mathematics,
Series volume
225
http://library.link/vocab/subjectName
  • Mathematics
  • Group theory
  • Topological groups
  • Group theory
  • Mathematics
  • Topological groups
Label
Lie Groups, by Daniel Bump, (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4757-4094-3
Instantiates
Publication
Antecedent source
file reproduced from original
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Haar Measure -- Schur Orthogonality -- Compact Operators -- The Peter-Weyl Theorem -- 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 -- 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
Dimensions
unknown
Extent
1 online resource (xi, 454 pages).
File format
unknown
Form of item
online
Isbn
9781475740943
Isbn Type
(electronic bk.)
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-1-4757-4094-3
Quality assurance targets
unknown
Reformatting quality
access
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)851840675
  • (OCoLC)ocn851840675
Label
Lie Groups, by Daniel Bump, (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4757-4094-3
Publication
Antecedent source
file reproduced from original
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Haar Measure -- Schur Orthogonality -- Compact Operators -- The Peter-Weyl Theorem -- 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 -- 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
Dimensions
unknown
Extent
1 online resource (xi, 454 pages).
File format
unknown
Form of item
online
Isbn
9781475740943
Isbn Type
(electronic bk.)
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-1-4757-4094-3
Quality assurance targets
unknown
Reformatting quality
access
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)851840675
  • (OCoLC)ocn851840675

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