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The Resource Lie Groups, by Daniel Bump, (electronic resource)
Lie Groups, by Daniel Bump, (electronic resource)
Resource Information
The item Lie Groups, by Daniel Bump, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Lie Groups, by Daniel Bump, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 PeterWeyl 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 FrobeniusSchur 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 coauthor 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)
 Language
 eng
 Extent
 1 online resource (xi, 454 pages).
 Contents

 Haar Measure
 Schur Orthogonality
 Compact Operators
 The PeterWeyl 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 JacobiTrudi 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
 Isbn
 9781475740943
 Label
 Lie Groups
 Title
 Lie Groups
 Statement of responsibility
 by Daniel Bump
 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 PeterWeyl 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 FrobeniusSchur 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 coauthor 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)
 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)
 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 PeterWeyl 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 JacobiTrudi 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
 10.1007/9781475740943
 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)
 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 PeterWeyl 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 JacobiTrudi 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
 10.1007/9781475740943
 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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