Cherednik algebras, W algebras and the equivariant cohomology of the\n moduli space of instantons on A²

2012/02/13 by Olivier Schiffmann, Schiffmann, Olivier, Éric Vasserot +1 · 6 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1202.2756

openalex publication_date 2012/02/13 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28

Abstract

We construct a representation of the affine W-algebra of gl_r on the\nequivariant homology space of the moduli space of U_r-instantons on A², and\nidentify the corresponding module. As a corollary we give a proof of a version\nof the AGT conjecture concerning pure N=2 gauge theory for the group SU(r).\nAnother proof has been announced by Maulik and Okounkov. Our approach uses a\nsuitable deformation of the universal enveloping algebra of the Witt algebra\nW_1+\∞, which is shown to act on the above homology spaces (for any r)\nand which specializes to all W(gl_r). This deformation is in turn constructed\nfrom a limit, as n tends to infinity, of the spherical degenerate double affine\nHecke algebra of GL_n.\n

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