The linear-resolution conjecture for two-row Specht ideals

Let $K$ be a field, let $R=K[x_1,\ldots,x_{2a+1}]$, and let $I^{\rm Sp}_{(a,a,1)}$ be the Specht ideal associated to the partition $(a,a,1)$. Linear-resolution conjecture. If

$$\operatorname{char}(K)=0,$$

then $R/I^{\rm Sp}_{(a,a,1)}$ has an $(a+2)$-linear resolution. The claim concerns the homological regularity of this family of Specht ideal quotients; the source gives no resolution status.