Finite-dimensionality conjecture for homology of degenerate minimal models

Let $p$ and $q$ be parameters, define

$$c_{p,q}=\frac{3}{2}\left(1-2\frac{(p-q)^2}{pq}\right),$$

and define

$$h_{p,q}^{m,n}=\frac{(np-mq)^2-(p-q)^2}{8pq}.$$

Let ${\mathcal L}_s$ be the Lie superalgebra introduced above, and let $L(c_{p,q},h_{p,q}^{m,n})$ denote the corresponding irreducible module. Finite-dimensionality conjecture. For every $q\in{\bf N}$,

$$\dim H_q({\mathcal L}_s,L(c_{p,q},h_{p,q}^{m,n}))<\infty.$$

The claim predicts finite-dimensional homology in the minimal-model setting, contrasting with the infinite-dimensional behavior noted for the special case discussed immediately before it. The supplied text gives no resolution, so the conjecture remains open.