Geodesic
Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2
Schiffmann, O.1  ; Vasserot, E.2 
1 Département de Mathématiques, Université de Paris-Sud Bâtiment 425, 91405, Orsay Cedex France
2 Département de Mathématiques, Université de Paris 7 175 rue du Chevaleret, 75013, Paris France
Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 213-342

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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, 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(𝔤𝔩 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 .

DOI : 10.1007/s10240-013-0052-3

Schiffmann, O. 1 ; Vasserot, E. 2

1 Département de Mathématiques, Université de Paris-Sud Bâtiment 425, 91405, Orsay Cedex France
2 Département de Mathématiques, Université de Paris 7 175 rue du Chevaleret, 75013, Paris France 
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     title = {Cherednik algebras, {W-algebras} and the equivariant cohomology of the moduli space of instantons on {<strong>A</strong>
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     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {213--342},
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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. Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 213-342. doi: 10.1007/s10240-013-0052-3

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