Modular Character Sheaves on Reductive Lie Algebras

TL;DR

This paper extends the theory of character sheaves on reductive Lie algebras to modular coefficients, providing new proofs and connections with the modular Springer correspondence, thus broadening the understanding of geometric representation theory.

Contribution

It introduces modular character sheaves on Lie algebras, reestablishes key results, and links them to the modular generalized Springer correspondence.

Findings

Extended character sheaves to modular coefficients

Reproved key results of Mirković

Connected to modular Springer correspondence

Abstract

Mirkovi\'c introduced the notion of character sheaves on a Lie algebra. Due to their simple geometric characterization, character sheaves on Lie algebras can be thought of as a simplified model for Lusztig's theory of character sheaves on algebraic groups. We extend the theory to the case of modular coefficients. Along the way, we will reprove some of Mirkovi\'c's results and provide connections with the modular generalized Springer correspondence of Achar, Juteau, Riche, and Williamson.