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
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We construct a representation of the affine W-algebra of 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 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 .
@article{PMIHES_2013__118__213_0,
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>
\protect\textsuperscript{2}}},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {213--342},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {118},
year = {2013},
doi = {10.1007/s10240-013-0052-3},
mrnumber = {3150250},
zbl = {1284.14008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-013-0052-3/}
}
TY - JOUR AU - Schiffmann, O. AU - Vasserot, E. TI - Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2 JO - Publications Mathématiques de l'IHÉS PY - 2013 SP - 213 EP - 342 VL - 118 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-013-0052-3/ DO - 10.1007/s10240-013-0052-3 LA - en ID - PMIHES_2013__118__213_0 ER -
%0 Journal Article %A Schiffmann, O. %A Vasserot, E. %T Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A 2 %J Publications Mathématiques de l'IHÉS %D 2013 %P 213-342 %V 118 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-013-0052-3/ %R 10.1007/s10240-013-0052-3 %G en %F PMIHES_2013__118__213_0
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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