© 1989
Linear Representations of Groups
Translated from the Russian by A. Iacob
- 4 Citations
- 2.4k Downloads
Part of the Modern Birkhäuser Classics book series (MBC)
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© 1989
Part of the Modern Birkhäuser Classics book series (MBC)
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 SU_{2} and SO_{3}. 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
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 SU_{2} and SO_{3}, 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)