Irreducibility conjecture for characteristic-zero Specht filtration factors

Let $F$ be a field of characteristic zero, let $\boldsymbol{\blambda}$ be a partition label, and let $\boldsymbol{\bT}$ range over the equivalence classes $\boldsymbol{\bT}$ of standard tableaux defined by the basis preorder. Let $S^{\boldsymbol{\blambda}}_{\boldsymbol{\bT}}$ be the corresponding filtration subquotient of the Specht module. Irreducibility conjecture. The module $S^{\boldsymbol{\blambda}}_{\boldsymbol{\bT}}$ is irreducible for every $\boldsymbol{\bT}$. This asserts irreducibility of all the filtration factors in characteristic zero; the source supplies no resolution status.