Kostka systems and exotic t-structures for reflection groups

TL;DR

This paper explores how Kostka systems associated with complex reflection groups can be used to construct exotic t-structures on derived categories, establishing derived equivalences and advancing the understanding of representation theory for reflection groups.

Contribution

It introduces a novel application of Kostka systems to build exotic t-structures and proves a derived-equivalence result, linking these structures to complex reflection groups.

Findings

Kostka systems enable the construction of exotic t-structures.

Derived equivalence between certain categories is established.

The approach advances the understanding of modules over reflection groups.

Abstract

Let W be a complex reflection group, acting on a complex vector space H. Kato has recently introduced the notion of a "Kostka system," which is a certain collection of finite-dimensional W-equivariant modules for the symmetric algebra on H. In this paper, we show that Kostka systems can be used to construct "exotic" t-structures on the derived category of finite-dimensional modules, and we prove a derived-equivalence result for these t-structures.