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OverviewOne of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram. The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincaré series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers. On these pages, the ideas and formulas due to J. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, H.S.M. Coxeter, V. Dlab and C.M. Ringel, V. Kac, J. McKay, T.A. Springer, B. Kostant, P. Slodowy, R. Steinberg, W. Ebeling and several other authors, as well as the author and his colleagues from Subbotin's seminar, are presented in detail. Several proofs seem to be new. Full Product DetailsAuthor: Rafael StekolshchikPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of hardcover 1st ed. 2008 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 0.454kg ISBN: 9783642096044ISBN 10: 3642096042 Pages: 240 Publication Date: 30 November 2010 Audience: Professional and scholarly , Professional & Vocational , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Out of print, replaced by POD We will order this item for you from a manufatured on demand supplier. Table of ContentsPreliminaries.- The Jordan normal form of the Coxeter transformation.- Eigenvalues, splitting formulas and diagrams Tp,q,r.- R. Steinberg’s theorem, B. Kostant’s construction.- The affine Coxeter transformation.ReviewsAuthor Information1980 - 1991, CAM (Center of Automation and Metrology), Academy of Sciences of Moldova, Project leader of experimental data processing. Research and development of programs and mathematical tools for Academy of Sciences of Moldova, 999 - 2007, ECI Telecom (Electronics Corporation of Israel), Israel, Project leader in the Network Management department. Research and development of algorithmes in the field of Communications and Big Systems. Tab Content 6Author Website:Countries AvailableAll regions |