The reducible Specht modules for the Hecke algebra $\mathcal{H}_{\mathbb{C},-1}(\mathfrak{S}_n)$

TL;DR

This paper advances the classification of reducible Specht modules for the Hecke algebra at q=-1 over characteristic zero fields, addressing a previously unresolved case in the theory.

Contribution

It proves half of a conjecture regarding the reducibility of Specht modules for the Hecke algebra at q=-1 in characteristic zero.

Findings

Partial proof of the conjecture for q=-1

Classification of reducible Specht modules in this case

Extension of existing classification results

Abstract

The reducible Specht modules for the Hecke algebra $\mathcal{H}_{\mathbb{F},q}(\mathfrak{S}_n)$ have been classified except when $q=-1$. We prove one half of a conjecture which we believe classifies the reducible Specht modules when $q=-1$ and $\mathbb{F}$ has characteristic 0.