Affine Gelfand-Tsetlin bases and affine Laumon spaces
Seminar Room 1, Newton Institute
Affine Laumon space P is the moduli space of parabolic sheaves of rank n on the product of 2 projective lines. The natural correspondences give rise to the action of affine Yangian of sl(n) on the equivariant cohomology of P. The resulting module M is isomorphic to the universal Verma module over the affine gl(n). The classes of torus fixed points form a basis of M which is an affine analogue of the classical Gelfand-Tsetlin basis. The Chern classes of tautological vector bundles on P can be computed in terms of the affine Yangian action on M.
This is a joint work with B.Feigin, A.Negut, and L.Rybnikov.