I will recall in the first part of the talk how generalized Kostka polynomials arise from the Weyl group action on cohomology of the flag variety. I will then explain how to define a bigraded version of Poisson homology that recovers these on the nilpotent cone via a formula suggested by Lusztig. As a consequence we obtain the gradings on zeroth Poisson homology of all finite W-algebras. The proof uses D-modules, the Springer resolution, and results of Hotta and Kashiwara. This is joint work with Bellamy.