Comet-shaped quiver varieties, Weyl group actions, and modified Kostka polynomials

TL;DR

This paper explores the algebraic structure of modified Kostka polynomials, linking them to Weyl group actions on the intersection cohomology of comet-shaped quiver varieties, revealing new insights into their interplay.

Contribution

It introduces a novel interpretation of structure coefficients of an algebra spanned by modified Kostka polynomials as traces of Weyl group actions on quiver variety cohomology.

Findings

Structure coefficients correspond to Weyl group trace values.

Weyl group actions are connected to the algebra of Kostka polynomials.

New geometric interpretation of Kostka polynomial-related algebra.

Abstract

We study an algebra spanned by modified Kostka polynomials. Particular structure coefficients of this algebra are interpreted as traces of some Weyl group actions on the intersection cohomology of comet-shaped quiver varieties.