图书介绍
Representations of Compact Lie Groups=紧李群的表示PDF|Epub|txt|kindle电子书版本网盘下载
- Theodor Brocker ; Tammo tom Dieck 著
- 出版社： Springer-Verlag
- ISBN：7506201275
- 出版时间：1999
- 标注页数：318页
- 文件大小：30MB
- 文件页数：331页
- 主题词：
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图书目录
CHAPTER Ⅰ Lie Groups and Lie Algebras1
1.The Concept of a Lie Group and the Classical Examples1
2.Left-Invariant Vector Fields and One-Parameter Groups11
3.The Exponential Map22
4.Homogeneous Spaces and Quotient Groups30
5.Invariant Integration40
6.Clifford Algebras and Spinor Groups54
CHAPTERⅡ Elementary Representation Theory64
1.Representations65
2.Semisimple Modules72
3.Linear Algebra and Representations74
4.Characters and Orthogonality Relations77
5.Representations of SU（2），SO（3），U（2），and O（3）.84
6.Real and Quaternionic Representations93
7.The Character Ring and the Representation Ring102
8.Representations of Abelian Groups107
9.Representations of Lie Algebras111
10.The Lie Algebra sl（2，？）115
CHAPTERⅢ Representative Functions123
1.Algebras of Representative Functions123
2.Some Analysis on Compact Groups129
3.The Theorem of Peter and Weyl133
4.Applications of the Theorem of Peter and Weyl136
5.Generalizations of the Theorem of Peter and Weyl138
6.Induced Representations143
7.Tannaka-Krein Duality146
8.The Complexification of Compact Lie Groups151
CHAPTER Ⅳ The Maximal Torus of a Compact Lie Group157
1.Maximal Tori157
2.Consequences of the Conjugation Theorem164
3.The Maximal Tori and Weyl Groups of the Classical Groups169
4.Cartan Subgroups of Nonconnected Compact Groups176
CHAPTER Ⅴ Root Systems183
1.The Adjoint Representation and Groups of Rank 1183
2.Roots and Weyl Chambers189
3.Root Systems197
4.Bases and Weyl Chambers202
5.Dynkin Diagrams209
6.The Roots of the Classical Groups216
7.The Fundamental Group，the Center and the Stiefel Diagram223
8.The Structure of the Compact Groups232
CHAPTER Ⅵ Irreducible Characters and Weights239
1.The Weyl Character Formula239
2.The Dominant Weight and the Structure of the Representation Ring249
3.The Multiplicities of the Weights of an Irreducible Representation257
4.Representations of Real or Quaternionic Type261
5.Representations of the Classical Groups265
6.Representations of the Spinor Groups278
7.Representations of the Orthogonal Groups292
Bibliography299
Symbol Index305
Subject Index307