李群(第2版)(英文版)

《李群(第2版)(英文版)》是一部研究生一年级 学习李群和李代数的教程，作者邦普采取了与许多教 材以紧李群的表示论作为理论基础不同的安排，并精 心挑选一系列材料，给读者提供更广阔的视野。本书 是第二版，在第一版的基础上增加了不少新内容，包 括更进一步讨论基本原理、使得一些证明更加流畅， 囊括了一些第一版没有涉及的结果和话题。

Preface Part Ⅰ Compact 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 Complexiflcation 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 Algebras 45 Gelfand Pairs 46 Hecke Algebras 47 The Philosophy of Cusp Forms 48 Cohomology of Grassmannians Appendix: Sage References Index