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Representations of Compact Lie Groups

  • Theodor Bröcker
  • Tammo tom Dieck

Part of the Graduate Texts in Mathematics book series (GTM, volume 98)

Table of contents

  1. Front Matter
    Pages i-x
  2. Theodor Bröcker, Tammo tom Dieck
    Pages 1-63
  3. Theodor Bröcker, Tammo tom Dieck
    Pages 64-122
  4. Theodor Bröcker, Tammo tom Dieck
    Pages 123-156
  5. Theodor Bröcker, Tammo tom Dieck
    Pages 157-182
  6. Theodor Bröcker, Tammo tom Dieck
    Pages 183-238
  7. Theodor Bröcker, Tammo tom Dieck
    Pages 239-298
  8. Back Matter
    Pages 299-316

About this book

Introduction

This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras, though mentioned occasionally, are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago. Prerequisites to the book are standard linear algebra and analysis, including Stokes' theorem for manifolds. The book can be read by German students in their third year, or by first-year graduate students in the United States. Generally speaking the book should be useful for mathematicians with geometric interests and, we hope, for physicists. At the end of each section the reader will find a set of exercises. These vary in character: Some ask the reader to verify statements used in the text, some contain additional information, and some present examples and counter­ examples. We advise the reader at least to read through the exercises.

Keywords

Groups Lie algebra lie group linear algebra manifold representation theory

Authors and affiliations

  • Theodor Bröcker
    • 1
  • Tammo tom Dieck
    • 2
  1. 1.Fachbereich MathematikUniversität RegensburgRegensburgFederal Republic of Germany
  2. 2.Mathematisches InstitutUniversität GöttingenGöttingenFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12918-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1985
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05725-0
  • Online ISBN 978-3-662-12918-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site