Conjecture on the weight variety of the maximal ideal at admissible affine $sl_3$ levels

Let $k=-3+\frac{2}{2m+1}$ with $m\geqslant 0$, let $V^k(sl_3)$ be the universal affine vertex operator algebra, and let $\mathcal I_k$ be its maximal ideal. Let $\mathcal V(I_k)$ denote the variety defined from this ideal, and let $\bar{\Lambda}_1,\bar{\Lambda}_2$ be the fundamental weights of $sl_3$. Conjecture.

$$\mathcal V(I_k)=\{t\bar{\Lambda}_1-\frac{2i}{2m+1}\bar{\Lambda}_2,\ t\bar{\Lambda}_2-\frac{2i}{2m+1}\bar{\Lambda}_1,\ t\bar{\Lambda}_1-(t+\frac{2i}{2m+1}+1)\bar{\Lambda}_2: t\in\mathbb C,\ i=0,1,\ldots,2m\}.$$

This is intended to describe the weight variety associated with the maximal ideal and complements the paper’s results on associated varieties of the simple affine vertex operator algebras $L_k(sl_3)$. The supplied text gives no resolution status, so whether this description is proved remains open in this record.