Equivariant Poincare series of filtrations

Abstract

We offer a new approach to a definition of an equivariant version of the Poincar\'e series. This Poincar\'e series is defined not as a power series, but as an element of the Grothendieck ring of $G$-sets with an additional structure. We compute this Poincar\'e series for natural filtrations on the ring of germs of functions on the plane $(\C^2,0)$ with a finite group representation.