The structure of projective indecomposable modules for $A_n$, $n\leq 12$

TL;DR

This paper details the structure of projective indecomposable modules for symmetric groups $A_n$ with $n \

Contribution

It provides a comprehensive description of these modules for $n \

Findings

Complete structures for $n \

Most structures for $n=12$ are determined, with few exceptions.

Advances understanding of modular representation theory of symmetric groups.

Abstract

This article gives the structure of all projective indecomposable modules in blocks with non-cyclic defect group for $n\leq 11$, and almost all in the case of $n=12$, leaving four simple modules for $p=2$ and one simple module for $p=3$.