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
Author
Author
Subject
Language
  • eng
  • eng
Summary
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes 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. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations
Member of
http://library.link/vocab/creatorName
Bump, Daniel
Dewey number
512.482
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
3DcxFdzIdpM
Language note
English
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
  • Topological Groups
  • Topological Groups, Lie Groups
Label
Lie Groups, by Daniel Bump, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (532 p.)
Form of item
online
Isbn
9781461480242
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4614-8024-2
Specific material designation
remote
System control number
  • (CKB)3710000000024281
  • (EBL)1466028
  • (SSID)ssj0001049515
  • (PQKBManifestationID)11682089
  • (PQKBTitleCode)TC0001049515
  • (PQKBWorkID)11019232
  • (PQKB)11421493
  • (DE-He213)978-1-4614-8024-2
  • (EXLCZ)993710000000024281
Label
Lie Groups, by Daniel Bump, (electronic resource)
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (532 p.)
Form of item
online
Isbn
9781461480242
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4614-8024-2
Specific material designation
remote
System control number
  • (CKB)3710000000024281
  • (EBL)1466028
  • (SSID)ssj0001049515
  • (PQKBManifestationID)11682089
  • (PQKBTitleCode)TC0001049515
  • (PQKBWorkID)11019232
  • (PQKB)11421493
  • (DE-He213)978-1-4614-8024-2
  • (EXLCZ)993710000000024281

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