Classification of indecomposable modules for finite group schemes of domestic representation type

TL;DR

This paper classifies indecomposable modules in the principal blocks of finite group schemes with domestic representation type, using support varieties, Clifford theory, and Auslander-Reiten quivers.

Contribution

It provides a comprehensive classification of modules for domestic group schemes, integrating support variety actions, Clifford theory, and quiver analysis.

Findings

Classification of modules in principal blocks achieved

Filtration and support variety techniques developed

Connections between Clifford theory and Auslander-Reiten quivers established

Abstract

We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford theory for certain group schemes and applications of Clifford theory for strongly group graded algebras to the structure of Auslander-Reiten quivers. The combination of these results leads to the classification of modules belonging to the principal blocks of the group algebra $k\mathcal{G}$.