Overview

This book gives an exposition of the fundamentals of the theory of linear representations of ?nite and compact groups, as well as elements of the t- ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the ?eld under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of ?nite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely - pliedbranchesof algebra. Practically every timethatgroupsareencountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. 0. Basic Notions 0. 1.

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9783034800624

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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)

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)

Author Information

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

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