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

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

2003-07-09

arxiv.org/abs/math/0307121v1

Mathematics

Representation Theory

LaTeX, 15 pages. Progress in Math. Birkhauser. To appear

Scientific paper

According to McKay (1980) the irreducible characters of finite subgroups 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 Poincare 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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