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We construct a representation of the affine W-algebra of gl_r on theequivariant homology space of the moduli space of U_r-instantons on A^2, andidentify the corresponding module. As a corollary we give a proof of a versionof 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 asuitable deformation of the universal enveloping algebra of the Witt algebraW_{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 constructedfrom a limit, as n tends to infinity, of the spherical degenerate double affineHecke algebra of GL_n.

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