Linear Representations of Groups: Translated from the Russian by A. Iacob (Modern Birkhäuser Classics) - Softcover

Vinberg, Ernest B.

Softcover

ISBN 10: 3034800622 ISBN 13: 9783034800624

Publisher: Birkhäuser, 2010

Synopsis

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.

About this title

About the Author

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

From the Back Cover

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

Edition details

• Publisher: Birkhäuser
• Publication date: 2010
• Language: English
• ISBN 10: 3034800622
• ISBN 13: 9783034800624
• Binding: Paperback
• Edition number: 1
• Number of pages: 152