On the derived Lusztig correspondence

TL;DR

This paper explores the relationship between derived categories of l-adic sheaves on certain algebraic stacks associated with a reductive group and its maximal torus, advancing understanding in geometric representation theory.

Contribution

It establishes a connection between the derived categories of l-adic sheaves on the stacks [Lie(T)/N] and [Lie(G)/G], providing new insights into their structural relationship.

Findings

Identifies a correspondence between the derived categories of sheaves on these stacks.

Provides a framework for understanding sheaf-theoretic connections in reductive groups.

Lays groundwork for further applications in geometric representation theory.

Abstract

Let $G$ be a connected reductive group, $T$ a maximal torus of $G$, and $N$ the normalizer of $T$ in $G$. In this paper we study the connection between the derived category of l-adic sheaves on the stack $[Lie(T)/N]$ and the derived category of $l$-adic sheaves on $[Lie(G)/G]$.