Applications of the trace formalism to Deligne-Lusztig theory

TL;DR

This paper applies the trace formalism to develop a categorical Jordan decomposition for finite groups of Lie type and analyzes the endomorphism algebra of the Gelfand-Graev representation, recovering known results.

Contribution

It introduces a categorical approach to Jordan decomposition and provides new insights into the endomorphism algebra of Gelfand-Graev representations.

Findings

Constructed categorical Jordan decomposition using trace formalism.

Recovered a known result on the endomorphism algebra of Gelfand-Graev representations.

Extended previous work with new applications in Deligne-Lusztig theory.

Abstract

This paper is a continuation of previous work of the author. We use the categorical trace formalism to give a construction of the 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.