# Irreducible restrictions of representations of symmetric and alternating groups in small characteristics

## TL;DR

This paper classifies how irreducible representations of symmetric and alternating groups behave when restricted to subgroups, especially in small characteristics, extending known results to more delicate cases.

## Contribution

It provides a detailed classification of irreducible restrictions in small characteristics, filling a gap in the understanding of subgroup representations of symmetric and alternating groups.

## Key findings

- Complete classification for small characteristics cases
- Extension of reduction theorems and dimension bounds
- Connection to the Aschbacher-Scott program

## Abstract

Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such classification 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. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.