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

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.