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Representations of Linear Groups

An Introduction Based on Examples from Physics and Number Theory

  • Textbook
  • © 2007

Overview

Authors:
  1. Rolf Berndt

    1. Department of Mathematics, University of Hamburg, Hamburg, Germany

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  • Gruppendarstellungen als Einstieg für Mathematiker und Physiker mit vielen Beispielen.

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Prologue: Some Groups and their Actions

    Pages 1-6

  3. Basic Algebraic Concepts for Group Representations

    Pages 7-22

  4. Representations of Finite Groups

    Pages 23-30

  5. Continuous Representations

    Pages 31-42

  6. Representations of Compact Groups

    Pages 43-57

  7. Representations of Abelian Groups

    Pages 59-62

  8. The Infinitesimal Method

    Pages 63-116

  9. Induced Representations

    Pages 117-172

  10. Geometric Quantization and the Orbit Method

    Pages 173-214

  11. Epilogue: Outlook to Number Theory

    Pages 215-260

  12. Back Matter

    Pages 261-270
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Keywords

About this book

This is an elementary introduction to the representation theory of real and complex matrix groups. The text is written for students in mathematics and physics who have a good knowledge of differential/integral calculus and linear algebra and are familiar with basic facts from algebra, number theory and complex analysis. The goal is to present the fundamental concepts of representation theory, to describe the connection between them, and to explain some of their background. The focus is on groups which are of particular interest for applications in physics and number theory (e.g. Gell-Mann's eightfold way and theta functions, automorphic forms). The reader finds a large variety of examples which are presented in detail and from different points of view. The examples motivate the general theory well covered already by the existing literature. Hence for complete proofs of most of the essential statements and theorems the reader is often referred to the standard sources. Plenty of exercises are included in the text. Some of these exercises and/or omitted proofs may give a starting point for a bachelor thesis and further studies in a master program.

Reviews

"This book is a very elementary introduction to some of the fundamental ideas in representation theory [...] Its emphasis on examples from physics and number theory makes it appealing to a broad audience."

Mathematical Reviews, 2008g

Authors and Affiliations

  • Department of Mathematics, University of Hamburg, Hamburg, Germany

    Rolf Berndt

About the author

Prof. Dr. Rolf Berndt, Department of Mathematics, University of Hamburg, Germany.

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