The Clifford Theory for Modular Representations of Finite Groups

Devjani Basu

The Clifford Theory for Modular Representations of Finite Groups

Representation Theory 2025-03-05 v1

Authors: Devjani Basu

Abstract

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 $SL_2(\mathbb{F}_p)$ in defining characteristic, with that of $GL_2(\mathbb{F}_p)$ using the modular Clifford theory.

Keywords

Clifford theory modular representations finite groups normal subgroups representation spaces

Cite

@article{arxiv.2503.02163,
  title  = {The Clifford Theory for Modular Representations of Finite Groups},
  author = {Devjani Basu},
  journal= {arXiv preprint arXiv:2503.02163},
  year   = {2025}
}

The Clifford Theory for Modular Representations of Finite Groups

Abstract

Keywords

Cite

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