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McKay’s correspondence and characters of finite subgroups of SU(2)

  • W. Rossmann
Chapter
Part of the Progress in Mathematics book series (PM, volume 220)

Abstract

According to MacKay [1980] the irreducible characters of finite sub-groups of SU(2) are in a natural 1-1 correspondence with the extended Coxeter-Dynkin graphs of type ADE. We show that the character values themselves can be given by an uniform formula, as special values of polynomials which arise naturally as numerators of Poincaré series associated to finite subgroups of SU(2) acting on polynomials in two variables. These polynomials have been the subject of a number of investigations, but their interpretation as characters has apparently not been noticed.

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • W. Rossmann
    • 1
  1. 1.University of OttawaOttawaCanada

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