Group Representation Theory

Copyright 2010 by Daniel Bump

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Introduction

Chapter 1: Group Theory

1.1 Review of Group Theory

1.3 Semidirect Products

1.4 Permutations

1.5 Group Actions

1.6 Sylow Theorems

1.8 Generators and Relations

1.9 The group GL(2)

1.10 Groups of Order 168

Chapter 2: Orthogonality and Characters

2.1 Hilbert Space Basics

2.2 Characters of Abelian Groups

2.3 Schur Orthogonality

2.5 Induction of Characters

2.6 Permutation Characters

2.7 Character Tables

Chapter 3: First Applications

3.1 The Character Ring

3.2 The Center and Derived Group

3.3 Frobenius Groups

Chapter 4: Induced Representations

4.1 Remarks on Brauer's Theorems

4.2 Induced Representations

4.3 Mackey Theory

4.4 Representations of GL(2)