© 1989

Linear Representations of Groups

Translated from the Russian by A. Iacob


Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-vii
  2. E. B. Vinberg
    Pages 1-12
  3. E. B. Vinberg
    Pages 13-54
  4. E. B. Vinberg
    Pages 55-71
  5. E. B. Vinberg
    Pages 73-92
  6. E. B. Vinberg
    Pages 93-116
  7. E. B. Vinberg
    Pages 117-132
  8. Back Matter
    Pages 133-146

About this book


This textbook contains a comprehensive and detailed exposition of the fundamentals of the representation theory of groups, especially of finite groups and compact groups. The exposition is based on the decomposition of the two-sided regular representation. This enables the author to give not only an abstract description of the representations but also their realizations in function spaces, which is important for physical applications. As an example, the theory of Laplace spherical functions is treated. Some basic ideas of the representation theory of Lie groups are also given, as well as all the representations of the groups SU2 and SO3. The book contains numerous examples and exercises, some with solutions.


------  Reviews


This book is a short modern introduction to representation theory of groups. (…) Basic examples and exercises enable the reader to change over to explicit calculations.

- Zentralblatt MATH


This is a short and very readable introduction to finite-dimensional representation theory. A preliminary chapter gives the general flavor of the theory describing many examples and emphasizing the “harmonic analysis” aspects. (…) There are many exercises in the text; at the end of the book there is a list of some answers and solutions. (…) Even though the book is very short, its exposition is clear and unhurried. By concentrating on essential matters the author succeeds in getting across many of the fundamental ideas of the theory.

- Mathematical Reviews


Laplace spherical functions Representation theory compact groups finite groups homomorphism representation theory of groups

Authors and affiliations

  1. 1., Chair of AlgebraMoscow UniversityMoscowRussian Federation

About the authors

Ernest B. Vinberg is a Professor of mathematics at the Moscow University.

Bibliographic information

  • Book Title Linear Representations of Groups
  • Book Subtitle Translated from the Russian by A. Iacob
  • Authors Ernest B. Vinberg
  • Series Title Modern Birkhäuser Classics
  • DOI
  • Copyright Information Birkhäuser Verlag 1989
  • Publisher Name Springer, Basel
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-0348-0062-4
  • eBook ISBN 978-3-0348-0063-1
  • Edition Number 1
  • Number of Pages VI, 146
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site


From the reviews:

“Vinberg’s book should be seen as preliminary to far more ambitious and weighty texts … . It takes the reader from raw basics, done very nicely, through the obligatory discussion of the regular representation … to some excellent stuff on SU2 and SO3, with a discussion of Laplace’s spherical functions thrown in. The presence of a huge number of guiding examples is a major asset … as is the large collection of exercises for the reader. It is indeed a marvelous introduction to representation theory!” (Michael Berg, The Mathematical Association of America, February, 2011)