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Field name	Details
Dewey Class	512.44
Title	Notes on Coxeter Transformations and the McKay Correspondence ([Ebook]) / by Rafael Stekolshchik.
Author	Stekolshchik, Rafael
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2008.
Physical Details	: online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9783540773993
Summary Note	One 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 PoincarÃ© 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.:
Contents note	Introduction -- Preliminaries -- 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 -- A. The McKay correspondence and the Slodowy correspondence -- B. Regularity conditions for representations of quivers -- C. Miscellanea -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-540-77399-3
Links to Related Works	Subject References: Algebra . Commutative Rings and Algebras . Group theory . Group Theory and Generalizations . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Stekolshchik, Rafael . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 512.44 . 512.44 (DDC 22) .

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Notes on Coxeter Transformations and the McKay Correspondence

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