An introduction to harmonic analysis on semisimple Lie groups

書誌事項

An introduction to harmonic analysis on semisimple Lie groups

V.S. Varadarajan

(Cambridge studies in advanced mathematics, 16)

Cambridge University Press, 1989

タイトル別名

Harmonic analysis on semisimple Lie groups

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注記

Bibliography: p. [310]-312

Includes index

内容説明・目次

内容説明

Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the subject in the context of special examples, without losing sight of its general flow and structure. The author begins with an account of compact groups and discusses the Harish-Chandra modules of SL(2,R) and SL(2,C). Professor Varadarajan then introduces the Plancherel formula and Schwartz spaces, and shows how these lead to the Harish-Chandra theory of Eisenstein integrals. The final sections are devoted to considering the irreducible characters of semi-simple Lie groups, including explicit calculations of SL(2,R). The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.

目次

  • Preface
  • 1. Introduction
  • 2. Compact groups: the work of Weyl
  • 3. Unitary representations of locally compact groups
  • 4. Parabolic induction, principal series representations, and their characters
  • 5. Representations of the Lie algebra
  • 6. The Plancherel formula: character form
  • 7. Invariant eigendistributions
  • 8. Harmonic analysis of the Schwartz space
  • Appendix 1. Functional analysis
  • Appendix 2. Topological groups
  • Appendix 3. Lie groups and Lie algebras
  • References
  • Index.

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