Speaker
Description
Affine Laumon spaces arise as moduli spaces of (SU(N)) instantons in the presence of a surface operator. Their equivariant cohomology was shown to form a Verma module over affine gl(n) for generic equivariant parameters. The torus fixed points provide a natural basis, which may be viewed as an affine analogue of the Gelfand--Tsetlin basis. We study a specialization of the equivariant parameters corresponding to a dominant, not necessarily integral, highest weight. In this case, the compact components of the fixed-point set are isolated points. We show that these points form a basis of an irreducible highest-weight module. In particular, this gives a combinatorial realization of admissible modules. On the level of characters, our construction provides a combinatorial interpretation of the Kac--Wakimoto character formula, generalizing the relation between semistandard Young tableaux and the Weyl character formula for Schur polynomials. This talk is based on joint work in progress with M. Bershtein, E. Mukhin, and L. Rybnikov.