McKay quivers and extended Dynkin diagrams

Abstract

Let k k be an algebraically closed field and G G a finite nontrivial group whose order is not divisible by the characteristic of k k . Associated with an m m -dimensional representation of G G is the McKay quiver, whose vertices correspond to the irreducible representations of G G . We show that if m = 2 m = 2 , then the underlying graph of the separated McKay quiver is a finite union of extended Dynkin diagrams.