K-theory of Springer varieties

Abstract

The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations, of a Springer variety $\mathcal{F}_{\lambda}$ of type $A$ associated to a nilpotent operator having Jordan canonical form whose block sizes form a weakly decreasing sequence $\lambda=(\lambda_1,\ldots, \lambda_l)$. Our description parallels the description of the integral cohomology ring of $\mathcal{F}_{\lambda}$ due to Tanisaki and also the equivariant analogue due to Abe and Horiguchi.