Refined Chern-Simons theory and Hilbert schemes of points on the plane

摘要

Aganagic and Shakirov propose a refinement of the SU(N) Chern-Simons theory for links in three manifolds with S~1-symmetry, such as torus knots in S3, based on deformation of the S and T matrices, originally found by Kirillov and Cherednik. We relate the large N limit of the S matrix to the Hilbert schemes of points on the affine plane. As an application, we find an explicit formula for the Euler characteristics of the universal sheaf, applied arbitrary Schur functor.