An Introduction to Harmonic Analysis on Semisimple Lie Groups

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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 topic.