Isomorphism conjecture for the edge-contraction quantum-group subquotient

Let $I$ be the index set before an edge contraction, let $\widehat I$ be the index set after the contraction, and let $\mathbf U_{I,\widehat I}$ be the subalgebra generated by the elements specified in the source. Let $\mathcal J_{I,\widehat I}$ be the two-sided ideal generated by $E_{i_-}E_{i_+}$ and $F_{i_+}F_{i_-}$, and let

$$\Phi:\mathbf U_{\widehat I}\longrightarrow \mathbf U_{I,\widehat I}/\mathcal J_{I,\widehat I}$$

be the surjective algebra homomorphism obtained from the edge-contraction embedding and the canonical quotient map.

Isomorphism conjecture. The map $\Phi$ is an isomorphism, hence $\mathbf U_I$ is a split subquotient of $\mathbf U_{\widehat I}$. This makes the conjectural subquotient statement precise for the quantum groups associated with an edge contraction. The supplied text does not give a proof or resolution of the conjecture.