Conférencier: Colin Ingalls (Carleton University)

Abstract: Fix a finite group G and a representation W, the McKay quiver has vertices given by irreducible representations V_i and dimHom_G(W⊗V_i,V_j) many arrows between V_i and V_j. We briefly present the history of McKay quivers and their applications in geometry and representation theory. Then we discuss recent descriptions of McKay quivers of reflection groups by M. Lewis, and work with E. Faber and R. Buchweitz applying results of Lustzig on McKay quivers to understand the relations of the basic model of the skew group ring.