Skip to main content
SpringerLink
Log in
Birkhäuser

Linear Representations of Groups

Translated from the Russian by A. Iacob

  • Book
  • © 1989

Overview

Authors:
  1. Ernest B. Vinberg

    1. , Chair of Algebra, Moscow University, Moscow, Russian Federation

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Brief, modern and very readable introduction to representation theory of groups
  • Clear and concentrating on the essentials
  • Provides numerous examples and exercises, some with solutions
  • Includes supplementary material: sn.pub/extras

Part of the book series: Modern Birkhäuser Classics (MBC)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Introduction

    • E. B. Vinberg
    Pages 1-12

  3. General Properties of Representations

    • E. B. Vinberg
    Pages 13-54

  4. Representations of Finite Groups

    • E. B. Vinberg
    Pages 55-71

  5. Representations of Compact Groups

    • E. B. Vinberg
    Pages 73-92

  6. Representations of Lie Groups

    • E. B. Vinberg
    Pages 93-116

  7. Appendices

    • E. B. Vinberg
    Pages 117-132

  8. Back Matter

    Pages 133-146
    Download chapter PDF
Back to top

Keywords

About this book

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.

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 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)

Authors and Affiliations

  • , Chair of Algebra, Moscow University, Moscow, Russian Federation

    Ernest B. Vinberg

About the author

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: https://doi.org/10.1007/978-3-0348-0063-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1989

  • Softcover ISBN: 978-3-0348-0062-4Published: 02 December 2010

  • eBook ISBN: 978-3-0348-0063-1Published: 23 November 2010

  • Series ISSN: 2197-1803

  • Series E-ISSN: 2197-1811

  • Edition Number: 1

  • Number of Pages: VI, 146

  • Topics: Algebra

Publish with us

Policies and ethics

Back to top

Search

Navigation