An Introduction to Harmonic Analysis on Semisimple Lie Groups

ISBN-13: 9780521663625 / Angielski / Miękka / 1999 / 328 str.

V. S. Varadarajan

Opis

Now in paperback, this graduate-level textbook is an excellent introduction to the representation theory of semi-simple Lie groups. Professor Varadarajan emphasizes the development of central themes in the context of special examples. He begins with an account of compact groups and discusses the Harish-Chandra modules of SL(2, R) and SL(2, C). Subsequent chapters introduce the Plancherel formula and Schwartz spaces, and show how these lead to the Harish-Chandra theory of Eisenstein integrals. The final sections consider the irreducible characters of semi-simple Lie groups, and include explicit calculations of SL(2, R). The book concludes with appendices sketching some basic topics and with a comprehensive guide to further reading. This superb volume is highly suitable for students in algebra and analysis, and for mathematicians requiring a readable account of the topi

Recenzje

"The author deserves gratitude for writing such a beautiful book for the beginner." Mathematical Reviews

Spis treści

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.