Classification of Procesi bundles

A Procesi bundle is a vector bundle on the Hilbert scheme of $n$ points on the plane. It was first constructed by Haiman who used it to prove the Schur positivity for Macdonald
polynomials. This bundle also provides a derived McKay equivalence for the Hilbert scheme. I will basically take the latter for an axiomatic description of a Procesi bundle. I will show that there are exactly two bundles with these properties: Haiman’s and its dual. The proof is based on the study of Rational Cherednik algebras. The talk is based on arXiv:1303.4617.