Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on An 2

摘要

We construct a representation of the affine W-algebra of ({mathfrak{g}}{mathfrak{l}}_{r}) on the equivariant homology space of the moduli space of U r -instantons, and we identify the corresponding module. As a corollary, we give a proof of a version of the AGT conjecture concerning pure N=2 gauge theory for the group SU(r).