Certain complex representations of $SL_2(\bar{\mathbb{F}}_q)$

Abstract

We introduce the representation category C (G) for a connected reductive algebraic group G which is defined over a finite field. We show that this category has many good properties for G = SL2( Fq). In particular, it is an abelian category and a highest weight category. Moreover, we classify the simple objects in C (G) for G = SL2( Fq).