Mathematics Seminar
Date: Friday, 22 August 2025
Time: 3:30 PM
Venue: Seminar Hall
K-theory of Springer Varieties
V Uma
IIT Madras.
22-08-25

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Abstract

Springer varieties $\mathcal{F}_{\lambda}$ are closed subvarieties of a complete flag variety $\mathcal{F}(\mathbb{C}^n)$ and were first introduced and studied by T. A. Springer. Springer showed that there is a natural action of the symmetric group $S_n$ on the rational cohomology of $\mathcal{F}_{\lambda}$ compatible with the standard action of $S_n$ on the rational cohomology of $\mathcal{F}$. The cohomology of Springer varieties was further studied by De Concini and Procesi and by Tanisaki who gave a presentation for the cohomology ring.

In this talk we shall 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 $N$ having Jordan canonical form whose block sizes form a weakly decreasing sequence $\lambda=(\lambda_{1},\ldots, \lambda_l)$. This is based on my recent joint work with Parameswaran Sankaran. Tohoku Math. J. 77 (2025), 93–104 DOI: 10.2748/tmj.20230509