出版社:世界图书出版公司北京公司
年代:2009
定价:58.0
本书作者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,以给予读者更广阔的视野。本书适用于数学系研究生一年级开设的李群及李代数课程。
Preface
Part Ⅰ: Compact Groups
1 Haar Measure
2 Schur Orthogonality
3 Compact Operators
4 The Peter-Weyl Theorem
Part Ⅱ: Lie Group Fundamentals
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 S1(2, C)
13 The Universal Cover
14 The Local Frobenius Theorem
15 Tori
16 Geodesics and Maximal Tori
17 Topological Proof of Cartans Theorem
18 The Weyl Integration Formula
19 The Root System
20 Examples of Root Systems
21 Abstract Weyl Groups
22 The Fundamental Group
23 Semisimple Compact Groups
24 Highest-Weight Vectors
25 The Weyl Character Formula
26 Spin
27 Complexification
28 Coxeter Groups
29 The Iwasawa Decomposition
30 The Bruhat Decomposition
31 Symmetric Spaces
32 Relative Root Systems
33 Embeddings of Lie Groups
Part Ⅲ: Topics
34 Mackey Theory
35 Characters of GL(n,C)
36 Duality between Sk and GL(n,C)
37 The Jacobi-Trudi Identity
38 Schur Polynomials and GL(n,C)
39 Schur Polynomials and Sk
40 Random Matrix Theory
41 Minors of Toeplitz Matrices
42 Branching Formulae and Tableaux
43 The Cauchy Identity
44 Unitary Branching Rules
45 The Involution Model for Sk
46 Some Symmetric Algebras
47 Gelfand Pairs
48 Hecke Algebras
49 The Philosophy of Cusp Forms
50 Cohomology of Grassmannians
References
Index
《李群(英文版)》Part I covers standard general properties of representations of compactgroups (including Lie groups and other compact groups, such as finite or p-adie ones). These include Schur orthogonality, properties of matrix coefficientsand the Peter-Weyl Theorem.
Part II covers the fundamentals of Lie gronps, by which I mean those sub-jects that I think are most urgent for the student to learn. These include thefollowing topics for compact groups: the fundamental group, the conjngacyof maximal tori (two proofs), and the Weyl character formula. For noncom-pact groups, we start with complex analytic groups that are obtained bycomplexification of compact Lie groups, obtaining the lwasawa and Bruhatdecompositions. These arc the reductive complex groups. They are of course aspecial case, bnt a good place to start in the noncompact world. More generalnoncompact Lie groups with a Cartan decomposition are studied in the lastfew chapters of Part II. Chapter 31, on symmetric spaces, alternates exampleswith theory, discussing the embedding of a noncompact symmetric space inits compact dnal, the boundary components and Bergman-Shilov boundaryof a symmetric tube domain, anti Cartans classification. Chapter 32 con-structs the relative root system, explains Satake diagrams and gives examplesillustrating the various phenomena that can occur, and reproves the Iwasawadecomposition, formerly obtained for complex analytic groups, in this moregeneral context. Finally, Chapter 33 surveys the different ways Lie groups canbe embedded in oue another.
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出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
版次 | 1版 | 印次 | 1 |
定价(元) | 58.0 | 语种 | 英文 |
尺寸 | 14 | 装帧 | 平装 |
页数 | 印数 | 1000 |
李群是世界图书出版公司北京公司于2009.08出版的中图分类号为 O152.5 的主题关于 李群-研究生-教材-英文 的书籍。