Formality for the nilpotent cone and a derived Springer correspondence

TL;DR

This paper extends the classical Springer correspondence to an equivalence between derived categories, linking Springer perverse sheaves and dg-modules related to the Weyl group, thus deepening the understanding of the nilpotent cone.

Contribution

It introduces a derived category framework for the Springer correspondence, connecting perverse sheaves on the nilpotent cone with dg-modules over a Weyl group-related dg-ring.

Findings

Establishes an equivalence between the triangulated category of Springer perverse sheaves and a derived category of dg-modules.

Provides a new perspective on the Springer correspondence through derived algebraic geometry.

Enhances the understanding of the structure of perverse sheaves in relation to Weyl group representations.

Abstract

Recall that the Springer correspondence relates representations of the Weyl group to perverse sheaves on the nilpotent cone. We explain how to extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group.