Representing Finite Groups

This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material.

Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful.

A separate solutions manual is available for instructors.

From the reviews:

“The book under review is an introduction to representation theory in the semisimple case. … Each chapter concludes with a fair number of exercises. … the book has been written carefully. Also, it gives the impression that it has been written enthusiastically. … the book is a welcome introduction for mathematics students or researchers looking for a first read in a fascinating subject.” (Gabriel Navarro, Mathematical Reviews, October, 2013)

“The purpose of this graduate text is to give a leisurely introduction to the representation theory of finite groups with an emphasis on semisimple algebras and modules over them. … Each chapter ends with a number of exercises. … The presentation of the material is friendly and inviting … . The reviewer believes that the book can do a fine job as an invitation to study representations of finite groups by giving a glimpse into many different aspects of the field.” (Thomas Michael Keller, Zentralblatt MATH, Vol. 1254, 2013)