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

Abstract

For $n\ge 5$ 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.

23 pages