# Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems

## TL;DR

This paper investigates how irreducible modules over alternating groups restrict to subgroups in small characteristics, providing new reduction theorems that narrow down possible subgroup-module configurations, especially in challenging small characteristic cases.

## Contribution

It introduces new reduction theorems for irreducible restrictions of alternating group modules in small characteristics, extending previous results known for larger characteristics.

## Key findings

- Reduction theorems restrict subgroup classes for irreducible restrictions
- Analysis specific to small characteristics requires new techniques
- Results contribute to the classification of maximal subgroups in finite classical groups

## Abstract

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the characteristic of the ground field is greater than $3$, but the small characteristics cases require a substantially more delicate analysis and new ideas. In view of our earlier work on symmetric groups we may consider only the restriction of irreducible modules over alternating groups which do not extend to symmetric groups. This work fits into the Aschbacher-Scott program on maximal subgroups of finite classical groups.