Tohoku Mathematical Journal
2025
March
SECOND SERIES VOL. 77, NO. 1

Tohoku Math. J.
77 (2025), 93-104

Title $K$-THEORY OF SPRINGER VARIETIES

Author Parameswaran Sankaran and Vikraman Uma

(Received January 19, 2022, revised May 8, 2023)
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.

Mathematics Subject Classification. Primary 55N15; Secondary 14M15, 19L19.
Key words and phrases. Springer varieties, flag varieties, $K$-theory, Chern character.

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