The $T(\lambda)$–$M(\lambda)$–$L(\gb\lambda)$ conjecture for minimal affinizations

Let $\lambda\in P^+$ be such that its extended support $\overline{\operatorname{supp}}(\lambda)$ does not contain a subdiagram of type $D_4$. Let $\gb\lambda\in\cal P_\mathbb A^{++}$ be such that $V_q(\gb\lambda)$ is a minimal affinization of $V_q(\lambda)$. Let $M(\lambda)$ and $T(\lambda)$ be the $\lie g[t]$-modules defined in the paper. $T(\lambda)$–$M(\lambda)$–$L(\gb\lambda)$ conjecture. One has

$$T(\lambda)\cong M(\lambda)\cong L(\gb\lambda).$$

This is presented as the expected generalization of an earlier proposition; the source does not state a resolution of it.