Last-row Schur module conjecture for the Veronese surface

For the $d$-uple Veronese embedding of $\mathbb P^2$, let $p:=d\binom{d+1}{2}$ and define

$$(a,b,c)=\left(\binom{d+2}{3}-1,\frac{1}{6}d(d^2+5),\binom{d+1}{3}-1\right).$$

Last-row Schur module conjecture. The last nonzero syzygy space is

$$K_{p,p+1}(\mathbb P^2,0;d)\cong \mathbf S_{(a,b,c)}.$$

This gives a Schur-functor analogue of a corresponding conjecture cited in the source; the specified $p$ is the maximum value for which $K_{p,p+1}(0;d)\ne0$. The paper presents this as a conjecture based on data, with no general proof stated.