Kazhdan-Laumon sheaves and Deligne-Lusztig representations

TL;DR

This paper links Kazhdan-Laumon sheaves on a reductive group over a finite field to Deligne-Lusztig representations, providing a new proof of a known result through cohomological comparison.

Contribution

It establishes a novel connection between Kazhdan-Laumon sheaves and Deligne-Lusztig varieties, offering a new proof of Dudas's result.

Findings

Cohomology of Kazhdan-Laumon sheaves matches that of Deligne-Lusztig varieties

Provides a new proof of Dudas's theorem

Enhances understanding of sheaf-theoretic approaches in representation theory

Abstract

Let $G$ be a reductive group over a finite field with a maximal unipotent subgroup $U$, we consider certain sheaves on $G/U$ defined by Kazhdan and Laumon and show that their cohomology produces the cohomology of the Deligne-Lusztig varieties. We then use this comparison to give a new proof of a result of Dudas.