An Introduction to Harmonic Analysis on Semisimple Lie Groups (Cambridge Studies in Advanced Mathematics, Series Number 16) by V. S. Varadarajan (PDF)

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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.

User’s Reviews

Editorial Reviews: Review “…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 Book Description Now in paperback, this graduate-level textbook introduces the representation theory of semi-simple Lie groups.

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