On the Endomorphism Algebra of Specht Modules in Even Characteristic

TL;DR

This paper investigates the structure of Specht modules over fields of characteristic 2, providing new descriptions of their endomorphism algebras and identifying families with one-dimensional endomorphism algebras.

Contribution

It introduces a novel approach to describe the endomorphism algebra of Specht modules and identifies infinite families with simple endomorphism algebra structures.

Findings

Infinite families of Specht modules with one-dimensional endomorphism algebra

New description of the endomorphism algebra in characteristic 2

Progress towards classifying decomposable Specht modules

Abstract

Over fields of characteristic $2$, Specht modules may decompose and there is no upper bound for the dimension of their endomorphism algebra. A classification of the (in)decomposable Specht modules and a closed formula for the dimension of their endomorphism algebra remain two important open problems in the area. In this paper, we introduce a novel description of the endomorphism algebra of the Specht modules and provide infinite families of Specht modules with one-dimensional endomorphism algebra.