%0 Journal Article
%T Cherednik algebras, W algebras and the equivariant cohomology of the moduli space of instantons on A^2
%A Olivier Schiffmann
%A Eric Vasserot
%J Mathematics
%D 2012
%I arXiv
%X We construct a representation of the affine W-algebra of gl_r on the equivariant homology space of the moduli space of U_r-instantons on A^2, and 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). Another proof has been announced by Maulik and Okounkov. Our approach uses a suitable deformation of the universal enveloping algebra of the Witt algebra W_{1+\infty}, which is shown to act on the above homology spaces (for any r) and which specializes to all W(gl_r). This deformation is in turn constructed from a limit, as n tends to infinity, of the spherical degenerate double affine Hecke algebra of GL_n.
%U http://arxiv.org/abs/1202.2756v2