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Graduate Studies in Mathematics 2004; 408 pp; hardcover Volume: 64 ISBN10: 0821835300 ISBN13: 9780821835302 List Price: US$75 Member Price: US$60 Order Code: GSM/64 See also: Representations of Semisimple Lie Algebras in the BGG Category \(\mathscr {O}\)  James E Humphreys Introduction to Representation Theory  Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob and Elena Yudovina  Isaac Newton encrypted his discoveries in analysis in the form of an anagram that deciphers to the sentence, "It is worthwhile to solve differential equations". Accordingly, one can express the main idea behind the orbit method by saying "It is worthwhile to study coadjoint orbits". The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for nonexperts and gives the first systematic, detailed, and selfcontained exposition of the method. It starts with a convenient "User's Guide" and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for nonexperts and a reference book for research mathematicians and mathematical physicists. Readership Graduate students and research mathematicians interested in representation theory. Reviews "The book offers a nicely written, systematic and readable description of the orbit method for various classes of Lie groups. ...should be on the shelves of mathematicians and theoretical physicists using representation theory in their work."  EMS Newsletter Table of Contents



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