Jordan decomposition, categorical traces and Deligne-Lusztig theory

Abstract

This paper is a continuation of the author's previous work. We use the categorical trace formalism to construct a categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we study the endomorphism algebra of the Gelfand-Graev representation and recover a result of Li and Shotton-Li.

Second version has been significantly enhanced. Comments are welcome