Elements of the Theory of Representations

1. Front Matter

   Pages I-XI

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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

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.

• Darstellung
• Group representation
• Lie algebra
• algebra
• cohomology
• commutative group
• finite group
• lie group
• locally compact group
• manifold
• matrix
• operator algebra
• ring
• transformation
• transformation group

• Moscow State University, USA

  Aleksandr A. Kirillov

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