Polynomials associated with fixed points on the instanton moduli space

Abstract

Using the Okounkov-Maulik stable map, we identify the equivariant cohomology of instanton moduli spaces with the space of polynomials on an infinite number of variables. We define the generalized Jack polynomials as the polynomials representing the classes of fixed points under this identification. Using the abelianization theorem of Shenfeld we derive the combinatorial formula for the expansion of generalized Jack polynomials in the basis of Schur polynomials.