Irreducible Restrictions of Representations of Symmetric Groups in Small Characteristics: Reduction Theorems

TL;DR

This paper investigates how irreducible representations of symmetric groups behave when restricted to subgroups in small characteristic fields, providing new reduction theorems that narrow down possible subgroup-module combinations.

Contribution

It extends known reduction results from large to small characteristic fields, offering new techniques for analyzing irreducible restrictions in these cases.

Findings

Reduction theorems for small characteristic cases

Narrowed classes of subgroups and modules for irreducible restrictions

Enhanced understanding within the Aschbacher-Scott program

Abstract

We study irreducible restrictions from modules over symmetric groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. Such results are 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. This work fits into the Aschbacher-Scott program on maximal subgroups of finite classical groups.