The vertices and sources of the natural simple module for the alternating group in even characteristic

TL;DR

None

Contribution

None

Abstract

For $n\geq 5$ the natural permutation module for the alternating group $\mathfrak{A}_n$ has a unique non-trivial composition factor, being called its natural simple module. We determine the vertices and sources of the natural simple $\mathfrak{A}_n$-module over fields of characteristic 2.