Deformation conjecture for the W B_l-algebra

Let $U_{q,p}(B_l^{(1)})$ be the elliptic algebra with level-$1$ currents $e_j(z)$ and $f_j(z)$, and let ${\cal F}_{\lambda,\xi,\kappa}(\Lambda+\mu,\mu)$ denote the modules appearing in the level-$1$ free-field realization, with $r$ and $\mu\in{\bf h}^*$ as in the source. A generating function commutes with a current modulo a total difference when their commutator is a total difference. Deformation conjecture. There exists a deformation of the $W\!B_l$-algebra such that

1. its generating functions commute with the level-$1$ elliptic currents $e_j(z)$ and $f_j(z)$ of $U_{q,p}(B_l^{(1)})$ modulo a total difference; equivalently, $e_j(z)$ and $f_j(z)$ at $c=1$ are the screening currents of the deformed $W\!B_l$-algebra;
2. for generic $r$ and $\mu\in{\bf h}^*$, ${\cal F}_{\lambda,\xi,\kappa}(\Lambda+\mu,\mu)$ is an irreducible module of that deformation.

The claim proposes a deformed $W\!B_l$-algebra whose screening currents control the level-$1$ elliptic representation theory. The supplied text gives the free-field character formulas and asserts the corresponding generic $W\!B_l$ Verma-module character agreement, but gives no resolution of this existence and irreducibility claim.