## Cherednik algebras, W algebras and the equivariant cohomology of the moduli space of instantons on A^2    [PDF]

Olivier Schiffmann, Eric Vasserot
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 prove the AGT conjecture
(in the massless case). 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, or
equivalently as a degeneration of the (spherical) Hall algebra of an elliptic
curve.
View original: http://arxiv.org/abs/1202.2756