Representation Theory of Finite Groups: a Guidebook

1. Front Matter

   Pages i-viii

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2. The Basics

   • David A. Craven

   Pages 1-14

3. Blocks and Their Characters

   • David A. Craven

   Pages 15-36

4. Modules

   • David A. Craven

   Pages 37-77

5. The Local-Global Principle

   • David A. Craven

   Pages 79-105

6. Blocks with Cyclic Defect Groups

   • David A. Craven

   Pages 107-131

7. Blocks with Non-cyclic Defect Groups

   • David A. Craven

   Pages 133-152

8. Clifford Theory

   • David A. Craven

   Pages 153-166

9. Representations of Symmetric Groups

   • David A. Craven

   Pages 167-212

10. Representations of Groups of Lie Type

    • David A. Craven

    Pages 213-255

11. Back Matter

    Pages 257-294

    PDF

This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures.

The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups.

Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.

• Group representation
• Representations of finite groups
• Representations of symmetric groups
• Finite groups of Lie type
• Block theory
• Modular representation theory
• Local-global conjectures
• Blocks with cyclic defect groups

“The book is intended for students and general readers. ... each of the chapters is followed by a series of exercises (83 in all), which are suitable for student seminars.” (A. S. Kondrat'ev, Mathematical Reviews, November, 2020)

“The book is highly recommended for researchers in representation and character theory of finite groups.” (Mohammad-Reza Darafsheh, zbMATH 1446.20002, 2020)

• School of Mathematics, University of Birmingham, Birmingham, UK

  David A. Craven

David A. Craven is a Royal Society Research Fellow and Senior Birmingham Fellow at the University of Birmingham. He has worked on a variety of areas within representations of groups, from the local-global conjectures to representations of symmetric groups, and groups of Lie type.