The classification conjecture for degenerate Verma modules over E(5,10)

Let $L=E(5,10)$, let $\mathfrak g_0\simeq \mathfrak{sl}_5(\mathbb C)$ be its degree-zero component, and let $F(n_1,n_2,n_3,n_4)$ be the finite-dimensional irreducible $\mathfrak g_0$-module with highest weight $(n_1,n_2,n_3,n_4)$. Write

$$M(n_1,n_2,n_3,n_4)=M(F(n_1,n_2,n_3,n_4))$$

for the corresponding generalized Verma module over $E(5,10)$. A Verma module is degenerate when it belongs to the exceptional list of modules admitting nontrivial morphisms. The classification conjecture. The complete list of degenerate Verma modules over $E(5,10)$ is

$$M(m,n,0,0),\qquad M(m,0,0,n),\qquad M(0,0,m,n)$$

for any $m,n\in\mathbb Z_+$. This conjectural list is attributed to the cited work of Kac and Rudakov and is intended to identify precisely the degenerate generalized Verma modules; the supplied text gives no resolution status beyond presenting it as a conjecture.