A Survey of the McKay Correspondence

Abstract

The McKay correspondence gives two constructions of simply laced Dynkin diagrams from a finite subgroup G of € SU(2)--the resolution graph of the quotient singularity of A2/G, and the McKay graph constructed from the nontrivial irreducible representations of G. We review the computation of the classical McKay correspondence for the binary dihedral group BD8, and discuss its generalizations. We also review the construction of tautological sheaves for the cyclic group as an example of a generalization to K-theory.