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Elements of the Theory of Representations

  • Book
  • © 1976

Overview

Authors:
  1. Aleksandr A. Kirillov

    1. Moscow State University, USA

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 220)

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Preliminary Facts

    1. Sets, Categories, Topology

      • Aleksandr A. Kirillov
      Pages 1-11

    2. Groups and Homogeneous Spaces

      • Aleksandr A. Kirillov
      Pages 11-24

    3. Rings and Modules

      • Aleksandr A. Kirillov
      Pages 24-35

    4. Elements of Functional Analysis

      • Aleksandr A. Kirillov
      Pages 35-62

    5. Analysis on Manifolds

      • Aleksandr A. Kirillov
      Pages 62-83

    6. Lie Groups and Lie Algebras

      • Aleksandr A. Kirillov
      Pages 83-107

  3. Basic Concepts and Methods of the Theory of Representations

    1. Representations of Groups

      • Aleksandr A. Kirillov
      Pages 108-115

    2. Decomposition of Representations

      • Aleksandr A. Kirillov
      Pages 115-129

    3. Invariant Integration

      • Aleksandr A. Kirillov
      Pages 129-139

    4. Group Algebras

      • Aleksandr A. Kirillov
      Pages 139-156

    5. Characters

      • Aleksandr A. Kirillov
      Pages 156-166

    6. Fourier Transforms and Duality

      • Aleksandr A. Kirillov
      Pages 166-181

    7. Induced Representations

      • Aleksandr A. Kirillov
      Pages 181-215

    8. Projective Representations

      • Aleksandr A. Kirillov
      Pages 215-225

    9. The Method of Orbits

      • Aleksandr A. Kirillov
      Pages 226-258

  4. Various Examples

    1. Finite Groups

      • Aleksandr A. Kirillov
      Pages 259-271

    2. Compact Groups

      • Aleksandr A. Kirillov
      Pages 271-278

    3. Lie Groups and Lie Algebras

      • Aleksandr A. Kirillov
      Pages 279-292

    4. Examples of Wild Lie Groups

      • Aleksandr A. Kirillov
      Pages 292-296
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About this book

The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the English-reading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans­ lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance.

Authors and Affiliations

  • Moscow State University, USA

    Aleksandr A. Kirillov

Bibliographic Information

  • Book Title: Elements of the Theory of Representations

  • Authors: Aleksandr A. Kirillov

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-66243-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1976

  • Softcover ISBN: 978-3-642-66245-4Published: 09 December 2011

  • eBook ISBN: 978-3-642-66243-0Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 318

  • Topics: Algebra

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