有限群的表示论

内容概要

Benjamin Steinberg（B.斯坦博格，加拿大）是数学领域知名学者，他的著作《有限群的表示论》是一部入门性教科书，深受读者欢迎。

书籍目录

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

作者简介

《有限群的表示论》是一部为大学高年级本科生和低年级研究生编写的教科书，内容主要涉及群表示论的各个方面。阅读本书所需背景知识包括线性代数，群论、环论基础知识，书中有意省略模理论，Wedderburn理论和张量积等内容，取而代之的加入离散傅里叶分析。

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