Certain complex representations of [formula omitted

Abstract

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