Representation Theory of Finite Groups

An Introductory Approach

  • Benjamin Steinberg

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Benjamin Steinberg
    Pages 1-1
  3. Benjamin Steinberg
    Pages 3-11
  4. Benjamin Steinberg
    Pages 13-25
  5. Benjamin Steinberg
    Pages 27-50
  6. Benjamin Steinberg
    Pages 51-70
  7. Benjamin Steinberg
    Pages 71-82
  8. Benjamin Steinberg
    Pages 83-96
  9. Benjamin Steinberg
    Pages 97-109
  10. Benjamin Steinberg
    Pages 111-115
  11. Benjamin Steinberg
    Pages 117-129
  12. Benjamin Steinberg
    Pages 131-152
  13. Back Matter
    Pages 153-157

About this book

Introduction

Representation Theory of Finite Groups presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linear algebra, group theory, and very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted. Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader.

The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside's pq-theorem and the dimension theorem, permutation representations, induced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probability and statistics, a chapter on random walks on finite groups serves as an illustration to link finite stochastics and representation theory. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject and the author provides motivation and a gentle style throughout the text. A number of exercises add greater dimension to the understanding of the subject and some aspects of a combinatorial nature are clearly shown in diagrams.

This text will engage a broad readership due to the significance of representation theory in diverse branches of mathematics, engineering, and physics, to name a few. Its primary intended use is as a one semester textbook for a third or fourth year undergraduate course or an introductory graduate course on group representation theory. The content can also be of use as a reference to researchers in all areas of mathematics, statistics, and several mathematical sciences.

Keywords

Burnside's Theorem character theory group representation induced representation permutation representation

Authors and affiliations

  • Benjamin Steinberg
    • 1
  1. 1., Department of MathematicsCity College of New YorkNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-0776-8
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-0775-1
  • Online ISBN 978-1-4614-0776-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book