Remarks on modular representations of finite groups of Lie type in non-defining characteristic

TL;DR

This paper discusses open problems and advances in the classification of modular irreducible representations of finite groups of Lie type in non-defining characteristic, focusing on principal series representations.

Contribution

It strengthens existing results on the classification of -modular principal series representations of finite groups of Lie type.

Findings

Addresses open problems in -modular representations

Provides a strengthened classification of principal series representations

Contributes to the understanding of modular representation theory of Lie type groups

Abstract

Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular irreducible representations of $G$. We also establish a strengthening of the results in [13] on the classification of the $\ell$-modular principal series representations of $G$.