- 作 者：（美）巴浦著
- 出 版 社：世界图书广东出版公司
- 出版年份：2009
- ISBN：9787510005008
- 标注页数：451 页
- PDF页数：40290653 页
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Part Ⅰ I: Compact Groups 3
1 Haar Measure 3
2 Schur Orthogonality 6
3 Compact Operators 17
4 The Peter-Weyl Theorem 21
Part Ⅱ: Lie Group Fundamentals 29
5 Lie Subgroups of GL(n, C) 29
6 Vector Fields 36
7 Left-Invariant Vector Fields 41
8 The Exponential Map 46
9 Tensors and Universal Properties 50
10 The Universal Enveloping Algebra 54
11 Extension of Scalars 58
12 Representations of sl(2, C) 62
13 The Universal Cover 69
14 The Local Frobenius Theorem 79
15 Tori 86
16 Geodesies and Maximal Tori 94
17 Topological Proof of Cartan's Theorem 107
18 The Weyl Integration Formula 112
19 The Root System 117
20 Examples of Root Systems 127
21 Abstract Weyl Groups 136
22 The Fundamental Group 146
23 Semisimple Compact Groups 150
24 Highest-Weight Vectors 157
25 The Weyl Character Formula 162
26 Spin 175
27 Complexification 182
28 Coxeter Groups 189
29 The Iwasawa Decomposition 197
30 The Bruhat Decomposition 205
31 Symmetric Spaces 212
32 Relative Root Systems 236
33 Embeddings of Lie Groups 257
Part Ⅲ: Topics 275
34 Mackey Theory 275
35 Characters of GL(n, C) 284
36 Duality between Sk and GL(n, C) 289
37 The Jacobi-Trudi Identity 297
38 Schur Polynomials and GL(n, C) 308
39 Schur Polynomials and Sk 315
40 Random Matrix Theory 321
41 Minors of Toeplitz Matrices 331
42 Branching Formulae and Tableaux 339
43 The Cauchy Identity 347
44 Unitary Branching Rules 357
45 The Involution Model for Sk 361
46 Some Symmetric Algebras 370
47 Gelfand Pairs 375
48 Hecke Algebras 384
49 The Philosophy of Cusp Forms 397
50 Cohomology of Grassmannians 428
References 438
Index 446