Classification conjecture for irreducible quasi-finite lowest-weight quantum toroidal modules

Let $\mathcal E_n$ denote the quantum toroidal algebra, and let $\mathcal H^{(\boldsymbol k),(\boldsymbol x,\boldsymbol y,\boldsymbol z)}_{\boldsymbol\alpha,\boldsymbol\beta,\boldsymbol\gamma}(\boldsymbol u)$ be the family of modules constructed from the indicated parameter tuples, where $\boldsymbol k$, $\boldsymbol x$, $\boldsymbol y$, $\boldsymbol z$, $\boldsymbol\alpha$, $\boldsymbol\beta$, $\boldsymbol\gamma$, and $\boldsymbol u$ are suitable parameters. Classification conjecture. Every irreducible, quasi-finite, lowest-weight $\mathcal E_n$-module is isomorphic to a module $\mathcal H^{(\boldsymbol k),(\boldsymbol x,\boldsymbol y,\boldsymbol z)}_{\boldsymbol\alpha,\boldsymbol\beta,\boldsymbol\gamma}(\boldsymbol u)$ with a suitable choice of parameters. The claim would classify all irreducible quasi-finite lowest-weight modules in the class considered by the paper; the supplied text gives no resolution status.