Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on <strong>A</strong>
<sup>2</sup>

Schiffmann, O.; Vasserot, E.

doi:10.1007/s10240-013-0052-3

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.

Résumé

We construct a representation of the affine W-algebra of $𝔤 𝔩_{r}$ 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 $W (𝔤 𝔩_{r})$ 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.

MR Zbl

DOI : 10.1007/s10240-013-0052-3

Affiliations des auteurs :

Schiffmann, O. ¹ ; Vasserot, E. ²

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     author = {Schiffmann, O. and Vasserot, E.},
     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},
     publisher = {Springer Berlin Heidelberg},
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     zbl = {1284.14008},
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     url = {http://archive.numdam.org/articles/10.1007/s10240-013-0052-3/}
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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. http://archive.numdam.org/articles/10.1007/s10240-013-0052-3/

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