McKay correspondence for the Poincar\'e series of Kleinian and Fuchsian   singularities
  We give a conceptual proof that the Poincar\'e series of the coordinate algebra of a Kleinian singularity and of a Fuchsian singularity of genus 0 is the quotient of the characteristic polynomials of two Coxeter elements. These Coxeter elements are interpreted geometrically, using triangulated categories and spherical twist functors. 
Wolfgang Ebeling, David Ploog