Equivariant $K$-theory of Springer Varieties

Abstract

The aim of this paper is to describe the topological equivariant $K$-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 $\lambda =({\lambda }_1,\dots ,{\lambda }_l)$. This parallels the description of the equivariant cohomology ring of ${\mathcal{F}}_{\lambda }$ due to Abe and Horiguchi and generalizes the description of ordinary topological $K$-ring of ${\mathcal{F}}_{\lambda }$ due to Sankaran and Uma \cite{su}.

26 pages