Decompositions of some Specht modules I

TL;DR

This paper analyzes the decomposition of certain Specht modules over characteristic 2 and Hecke algebras at q=-1, providing new insights into their indecomposable summands.

Contribution

It extends the decomposition results of Specht modules to characteristic 2 and Hecke algebras at q=-1, including hook-labeled modules.

Findings

Decomposition of Specht modules into indecomposables in characteristic 2

Identification of Specht modules labeled by hooks as indecomposable

Extension of results to Hecke algebras at q=-1

Abstract

We give a decomposition as a direct sum of indecomposable modules of several types of Specht modules in characteristic $2$. These include the Specht modules labelled by hooks, whose decomposability was considered by Murphy. Since the main arguments are essentially no more difficult for Hecke algebras at parameter $q=-1$, we proceed in this level of generality.