Nonexistence conjecture for strange subquotients

Let $L$ be a simple $\mathfrak{g}$-module and let $V$ be a finite-dimensional $\mathfrak{g}$-module. A strange subquotient of $V\otimes_{\mathbb{C}}L$ is a non-simple subquotient having Gelfand–Kirillov dimension $\operatorname{GKdim}(L)$ but no simple subquotient of that dimension. Strange-subquotient conjecture. Strange subquotients of $V\otimes_{\mathbb{C}}L$ do not exist. The paper explains that there are no strange quotients and, for holonomic $L$, no strange submodules; the conjecture rules out the remaining possibility of strange subquotients in general.