Notes on Coxeter Transformations and the McKay Correspondence

  • Rafael Stekolshchik

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

About this book


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.

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.


Cartan matrix Coxeter transformation Dynkin diagram Eigenvalue Matrix McKay correspondence Poincare series Representation theory

Authors and affiliations

  • Rafael Stekolshchik
    • 1
  1. 1.Tel-AvivIsrael

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