Let G be a finite subgroup of GLn(K) for a field K whose characteristic does not divide the order of G. The group G acts linearly on the polynomial ring S in n variables over K. When G is generated by reflections, then the discriminant D of the group action of G on S is a hypersurface with a singular locus of codimension 1. In this talk we give a natural construction of a non-commutative resolution of singularities of the coordinate ring of D as a quotient of the skew group ring A = S ∗ G by the idempotent e corresponding to the trivial representation. We will explain how this can be seen in some sense as a McKay correspondence for reflection groups.
This is joint work with Ragnar-Olaf Buchweitz and Colin Ingalls.
This video was produced by Syracuse University Department of Mathematics as part of ICRA 2016.
