Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2
By O. Schiffmann, E. Vasserot. Publications mathématiques (Bures-sur-Yvette), 2012
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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 Ur-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 W1+∞, 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 GLn.
Subfields: Algebra and Number Theory, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/ec85c95c1a3680bfa5e56d3858b05fa2188f9c39
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Citations in the corpus
- The affine Yangian of gl1 revisited (2014, unknown): “1 ···x j n= Y 1≤a<b≤n (xa−xb−h1)(xb−xa−h1) (xa−xb)2 Y 1≤s≤n xj s. Let {K(a;j) −n } j∈Z + n∈N be analogous elements in the opposite algebra (S a)opp. The following result has been already proved in [SV2] (we refer the reader to Appendix E for an alternative proof). Theorem 8.6. The vector vH r is ”
- The integrality conjecture and the cohomology of preprojective stacks (2016, background): “The passage from torsion freeness to all of the other statements of the theorem is as explained in [42], so we focus on torsion-freeness.”
- Coproduct for Yangians of affine Kac–Moody algebras (2017, unknown): “ TB15]. This affine Yangian was shown in [AS13] to be isomorphic to a certain algebra SHc which is a sort of stable limit of spherical trigonometric Cherednik algebras of type glℓ and was introduced in [SV13] where it was used to prove a version of the AGT-conjecture. The algebra SHc, and thus the affin”