The tensor-product decomposition conjecture for the current algebra

Let $\mathcal A_q$ be the current algebra, let $\mathcal O_q$ be the q-Onsager algebra with generators $A,B$, let $\{\tilde g_{k+1}\}_{k\in\mathbb N}\subseteq\mathcal J$ be the sequence from the lower-generator uniqueness conjecture, and let $\lambda_1,\lambda_2,\ldots$ be commuting indeterminates. Tensor-product decomposition conjecture. There exists an algebra isomorphism

$$\sharp:\mathcal A_q\to\mathcal O_q\otimes\mathbb F[\lambda_1,\lambda_2,\ldots]$$

that sends $\mathcal W_0\mapsto A\otimes1$, $\mathcal W_1\mapsto B\otimes1$, and

$$\tilde G_1\mapsto\tilde g_1+\lambda_1,$$

with the subsequent images specified by the displayed formulas for $\tilde G_2$, $\tilde G_3$, and $\tilde G_4$ in the source.

This conjecture depends on the preceding uniqueness conjecture and would decompose the current algebra into the q-Onsager algebra and a polynomial algebra. Its resolution is not supplied.