The quantum Hall algebra isomorphism conjecture for the positive loop algebra

Let $\mathbf{U}^+$ be the $\mathbb{C}_v$-subalgebra of $\mathbf{U}_v(L\mathfrak{gl}_p)$ generated by $\mathbf{U}_0^+$ and $h_{0,l}$ for $l>0$, where $\mathbf{U}_0^+$ is generated by $\epsilon_0$ and $x^+_{i,0}$ for $i=1,\ldots,p-1$, and let $E_0,E_i$ and $\mathbf{h}_l$ denote the corresponding generators of $\mathbf{H}_p$. The quantum Hall algebra isomorphism conjecture. The assignment $\epsilon_0\mapsto E_0$, $x^+_{i,0}\mapsto E_i$, $h_{0,l}\mapsto\mathbf{h}_l$ extends to an isomorphism of $\mathbb{C}(v)$-algebras

$$\mathbf{U}^+\otimes \mathbb{C}(v)\stackrel{\sim}{\to}\mathbf{H}_p\otimes \mathbb{C}(v).$$

This is presented as the quantum analogue of the preceding classical isomorphism, but the supplied text gives no resolution status.