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 $\lambda =({\lambda }_1,\dots ,{\lambda }_l)$. 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.

15 pages, Accepted for publication in Tohoku Mathematical Journal