Abstract
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).
Our approach uses a deformation of the universal enveloping algebra of W 1+∞, which acts on the above homology space and which specializes to \(W({\mathfrak{g}}{\mathfrak{l}}_{r})\) for all r. This deformation is constructed from a limit, as n tends to ∞, of the spherical degenerate double affine Hecke algebra of GL n .
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This research was partially supported by the ANR grant number ANR-10-BLAN-0110.
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Schiffmann, O., Vasserot, E. Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2 . Publ.math.IHES 118, 213–342 (2013). https://doi.org/10.1007/s10240-013-0052-3
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DOI: https://doi.org/10.1007/s10240-013-0052-3