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

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 $G$.

11 pages; this note corresponds to my talk at the 10th RAQ conference in Nagoya (August, 2010). It will appear in the proceedings, AMS Contemporary Mathematics