Module extension conjecture for finite-dimensional irreducible \widetilde \square_q-modules

Let $V$ be a finite-dimensional irreducible $\widetilde \square_q$-module, where $\widetilde \square_q$ and $\boxtimes_q$ are the algebras appearing in the paper, with generators $x_i$ and $x_{i-1,i}$ indexed by $i\in\mathbb Z_4$. Module extension conjecture. The vector space $V$ becomes a $\boxtimes_q$-module such that, for each $i\in\mathbb Z_4$, the action of $x_i$ on $V$ is a scalar multiple of the action of $x_{i-1,i}$ on $V$, and this $\boxtimes_q$-module is irreducible. This proposes an extension of irreducible finite-dimensional $\widetilde \square_q$-modules to irreducible $\boxtimes_q$-modules; the supplied text gives no evidence that it has been resolved.