The center and q-Onsager factorization conjecture for the current algebra

Let $\mathcal A_q$ be the current algebra, let $Z(\mathcal A_q)$ denote its center, let $\Delta_{k+1}\in Z(\mathcal A_q)$, and let $\langle\mathcal W_0,\mathcal W_1\rangle$ be the subalgebra generated by $\mathcal W_0,\mathcal W_1$. Let $\mathcal O_q$ be the $q$-Onsager algebra with generators $A,B$. Center and factorization conjecture. The following hold: (i) $\mathbb F[\lambda_1,\lambda_2,\ldots]\to Z(\mathcal A_q)$, $\lambda_{k+1}\mapsto\Delta_{k+1}$, is an algebra isomorphism; (ii) $\mathcal O_q\to\langle\mathcal W_0,\mathcal W_1\rangle$, $A\mapsto\mathcal W_0$, $B\mapsto\mathcal W_1$, is an algebra isomorphism; and (iii) multiplication induces an algebra isomorphism

$$\langle\mathcal W_0,\mathcal W_1\rangle\otimes Z(\mathcal A_q)\to\mathcal A_q,$$

$u\otimes v\mapsto uv$.

This conjecture describes the center and expresses the current algebra as a product of its q-Onsager subalgebra and center. No resolution is supplied in the source.