Notes on Coxeter Transformations and the McKay Correspondence
Publication Date: 2008
ISBN: 978-3-540-77399-3
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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 Poincaré series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.
Subject: Mathematics and Statistics, Cartan matrix, Coxeter transformation, Dynkin diagram, Eigenvalue, Matrix, McKay correspondence, Poincare series, Representation theory
