Tuesday, February 14, 2012

1202.2756 (Olivier Schiffmann et al.)

Cherednik algebras, W algebras and the equivariant cohomology of the
moduli space of instantons on A^2

Olivier Schiffmann, Eric Vasserot
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 on A^2, and
identify the corresponding module. As a corollary we prove the AGT conjecture
(in the massless case). Our approach uses a suitable deformation of the
universal enveloping algebra of the Witt algebra W_{1+\infty}, which is shown
to act on the above homology spaces (for any r) and which specializes to all
W(gl_r). This deformation is in turn constructed from a limit, as n tends to
infinity, of the spherical degenerate double affine Hecke algebra of GL_n, or
equivalently as a degeneration of the (spherical) Hall algebra of an elliptic
View original: http://arxiv.org/abs/1202.2756

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