Abstract:

I will describe the functionals (and more generally, distributions) on symmetric powers of symplectic varieties which are invariant under Hamiltonian flow. These are related to quotient singularities of type A_{n-1} = S_n. I will describe also the answer for type D_n. I will then derive corollaries concerning finite-dimensional representations and prime ideals of quantizations of these singular varieties. Finally, I will explain how these results confirm conjectures on symplectic resolutions of affine Poisson varieties. Most of this is joint work with P. Etingof.