Applications of the trace formalism to Deligne-Lusztig theory

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.

💡 Research Summary

The paper develops two major applications of the categorical trace formalism to the representation theory of finite groups of Lie type. Building on the author’s earlier work