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

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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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Authors and Affiliations

  1. Département de Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    O. Schiffmann

  2. Département de Mathématiques, Université de Paris 7, 175 rue du Chevaleret, 75013, Paris, France

    E. Vasserot

Authors
  1. O. Schiffmann
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  2. E. Vasserot
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Correspondence to E. Vasserot.

Additional information

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

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