《有限群的表示論》是2016年世界圖書出版公司出版的著作，作者是Benjamin Steinberg 。
基本介紹
- 書名：《有限群的表示論》
- 作者：Benjamin Steinberg
- ISBN：9787519210427
- 出版社：世界圖書出版公司
- 出版時間：2016-5-1
內容簡介,目錄,
內容簡介
《有限群的表示論》是一部為大學高年級本科生和低年級研究生編寫的教科書，內容主要涉及群表示論的各個方面。閱讀本書所需背景知識包括線性代數，群論、環論基礎知識，書中有意省略模理論，Wedderburn理論和張量積等內容，取而代之的加入離散傅立葉分析。
目錄
1 Introduction
2 Review of Linear Algebra
2.1 Basic Definitions and Notation
2.2 Complex Inner Product Spaces
2.3 Further Notions from Linear Algebra
3 Group Rep resentations
3.1 Basic Definitions and First Examples
3.2 Maschke's Theorem and Complete Reducibility
4 Character Theory and the Orthogonality Relations
4.1 Morphisms of Representations
4.2 The Orthogonality Relations
4.3 Characters and Class Functions
4.4 The Regular Representation
4.5 Representations of Abelian Groups
5 Fourier Analysis on Finite Groups
5.1 Periodic Functions on Cyclic Groups
5.2 The Convolution Product
5.3 Fourier Analysis on Finite Abelian Groups
5.4 An Application to Graph Theory
5.5 Fourier Analysis on Non—abelian Groups
6 Bumside's Theorem
6.1 A Little Number Theory
6.2 The Dimension Theorem
6.3 Burnside's Theorem
7 Group Actions and Permutation Representations
7.1 Group Actions
7.2 Permutation Representations
7.3 The Centralizer Algebra and Gelfand Pairs
8 Induced Representations
8.1 Induced Characters and Frobenius Reciprocity
8.2 Induced Representations
8.3 Mackey's Irreducibility Criterion
9 Another Theorem of Burnside
9.1 Conjugate Represen tations
10 Representation Theory of the Symmetric Group
10.1 Partitions and Tableaux
10.2 Constructing thelneducible Representations
11 Probability and Random Walks on Groups
11.1 Probabilities on Groups
11.2 Random Walks on Finite Groups
11.3 CardShuffling
11.3.1 The Riffle Shuffle
11.4 The Spectrum and the Upper Bound Lemma
References
Index
