The Duals of the 2-Modular Irreducible Modules of the Alternating Groups

TL;DR

This paper characterizes the dual modules of all irreducible representations of alternating groups over fields with characteristic 2, providing a complete understanding of their duality properties.

Contribution

It explicitly determines the dual modules of all irreducible modules of alternating groups in characteristic 2, a previously unresolved problem.

Findings

Complete classification of dual modules in characteristic 2

Explicit descriptions of duality for irreducible modules

Advances understanding of modular representation theory of alternating groups

Abstract

We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.