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.
Rezensionen / Stimmen
"...expository writing traces the historical development of the subject and makes this a very readable account." American Mathematical Monthly "...the best introduction to harmonic analysis on semisimple Lie groups from the analytic viewpoint." Joseph A. Wolf, Bulletin of the American Mathematical Society "The author deserves gratitude for writing such a beautiful book for the beginner." Mathematical Reviews
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 20 mm
Gewicht
ISBN-13
978-0-521-66362-5 (9780521663625)
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Schweitzer Klassifikation
Autor*in
University of California, Los Angeles
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.
