Springer, Procesi and Cherednik

The talk is based on a joint work with Pablo Boixeda Alvarez. We study equivariant Borel-Moore homology of certain affine Springer fibers and relate them to global sections of suitable vector bundles arising from Procesi bundles on Q-factorial terminalizations of symplectic quotient singularities. We use this relation to derive some information on the center of the principal block of the small quantum group. Our main technique is based on studying bimodules over Cherednik algebras.