By V. S. Varadarajan

Now in paperback, this graduate-level textbook is a wonderful advent to the illustration concept of semi-simple Lie teams. Professor Varadarajan emphasizes the improvement of relevant issues within the context of unique examples. He starts with an account of compact teams and discusses the Harish-Chandra modules of SL(2,R) and SL(2,C). next chapters introduce the Plancherel formulation and Schwartz areas, and exhibit how those bring about the Harish-Chandra conception of Eisenstein integrals. the ultimate sections examine the irreducible characters of semi-simple Lie teams, and contain specific calculations of SL(2,R). The booklet concludes with appendices sketching a few easy subject matters and with a entire consultant to extra analyzing. This outstanding quantity is extremely appropriate for college students in algebra and research, and for mathematicians requiring a readable account of the subject.

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Now in paperback, this graduate-level textbook is a superb advent to the illustration conception of semi-simple Lie teams. Professor Varadarajan emphasizes the improvement of significant issues within the context of specified examples. He starts with an account of compact teams and discusses the Harish-Chandra modules of SL(2,R) and SL(2,C).

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**Extra info for An Introduction to Harmonic Analysis on Semisimple Lie Groups (Cambridge Studies in Advanced Mathematics)**

**Example text**

23. L. E. Dickson, Linear groups with an exposition of the Galois ﬁeld theory, New York, Dover, 1958. 24. M. Aschbacher, On the maximal subgroups of the ﬁnite classical groups, Invent. , 76, N 3 (1984), 469—514. 25. P. B. Kleidman, The maximal subgroups of the ﬁnite 8-dimensional orthogonal groups P Ω+ 8 (q) and of their automorphism groups, J. Algebra, 66, N 1 (1987), 173—242. 26. D. Gorenstein, K. Harada, Finite simple groups of low rank and the families G2 (q), D42 (q), q odd, Bull. Am. Math.

16, пр. Ак. Коптюга, 4, Институт математики Институт математики СО РАН. и механики УрО РАН.

P. B. Kleidman, The maximal subgroups of the ﬁnite 8-dimensional orthogonal groups P Ω+ 8 (q) and of their automorphism groups, J. Algebra, 66, N 1 (1987), 173—242. 26. D. Gorenstein, K. Harada, Finite simple groups of low rank and the families G2 (q), D42 (q), q odd, Bull. Am. Math. , 77, N 6 (1971), 829—862. Поступило 8 августа 2001 г. Адреса авторов: Окончательный вариант 17 ноября 2002 г. КОНДРАТЬЕВ Анатолий Семенович, МАЗУРОВ Виктор Данилович, РОССИЯ, РОССИЯ, 620066, г. Екатеринбург, 630090, г.