The Clifford Theory for Modular Representations of Finite Groups

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on an explicit analysis of the representation spaces and their decompositions. We also analyze the relation between the modular representations of $S{L}_2({\mathbb{F}}_p)$ in defining characteristic, with that of $G{L}_2({\mathbb{F}}_p)$ using the modular Clifford theory.