On the Submodule Structure of Hook Specht Modules in Characteristic 2 II

TL;DR

This paper classifies uniserial 2-part Young modules and decomposes hook Specht modules into uniserial summands in characteristic 2, advancing understanding of their submodule structures.

Contribution

It provides a detailed classification of uniserial modules and decompositions of hook Specht modules in characteristic 2, extending previous research.

Findings

Identified which 2-part Young modules are uniserial in characteristic 2

Determined when hook Specht modules decompose into uniserial summands

Extended classification results from prior work

Abstract

We classify which 2-part Young modules in characteristic 2 are uniserial, and which hook Specht modules in characteristic 2 are direct sums of uniserial summands. This is a continuation of the author's previous work [arxiv:2405.02039].