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Equivariant $K$-theory of Springer Varieties (2301.01886v2)
Published 5 Jan 2023 in math.KT, math.AG, and math.AT
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 $\lambda=(\lambda_1,\ldots, \lambda_l)$. 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}.