Formality and Lusztig's generalized Springer correspondence

TL;DR

This paper establishes a derived equivalence linking blocks of sheaves on the nilpotent cone with modules over a degenerated Lusztig's graded Hecke algebra, advancing the understanding of the generalized Springer correspondence.

Contribution

It introduces a derived version of the generalized Springer correspondence and constructs a mixed geometric category related to Lusztig's algebra.

Findings

Proves a derived equivalence between sheaf categories and dg modules.

Constructs a mixed geometric category for the setting.

Provides new insights into Lusztig's graded Hecke algebra and Springer correspondence.

Abstract

We prove a derived equivalence between each block of the derived category of sheaves on the nilpotent cone and the category of differential graded modules over a degeneration of Lusztig's graded Hecke algebra. Along the way, we construct and study a mixed version of the geometric category. This work can be viewed as giving a derived version of the generalized Springer correspondence.