Quantum vertex algebra structure conjecture for the induced extension of cmathfrak{d}

Let $cmathfrak{d}$ be the cotangent Lie algebra under consideration, let $cwidehat{DY}_{chbar,cell}(cmathfrak{d})$ be its completed double Yangian, and define

$$\mathcal D_{G,k}=\bigoplus_{V\in\operatorname{Irrd}(G)}\mathcal M_V\otimes V^*$$

with $cmathcal M_V$ the induced module described in the source. Let $cmathcal V_1(cmathfrak{d})$ denote the corresponding quantum vertex algebra. Quantum vertex algebra structure conjecture. The $cwidehat{DY}_{chbar,cell}(cmathfrak{d})$-module $cmathcal D_{G,k}$ has the structure of a quantum vertex algebra extending the quantum vertex algebra structure of $cmathcal V_1(cmathfrak{d})$. This would quantize the extension of the affine vertex algebra associated with chiral differential operators on $G$; the source gives no proof or resolution.