Modular Character Sheaves on Reductive Lie Algebras

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.