Quantized multiplication conjecture for truncated shifted Yangians

Let $\lambda$ be a dominant coweight and let $\mu\leq\lambda$ be a coweight such that $\mu+\alpha_i^\vee\leq\lambda$. Let $Y_\mu^\lambda(\mathbf{R})$ be the truncated shifted Yangian, and let $E_i^{(1)}$ be its indicated generator. Quantized multiplication conjecture. There exists an isomorphism

$$Y_\mu^\lambda(\mathbf{R})[(E_i^{(1)})^{-1}]\xrightarrow{\sim}Y_{-\alpha_i^\vee}^0\otimes Y_{\mu+\alpha_i^\vee}^\lambda(\mathbf{R})$$

that fits into the commutative diagram obtained from the localization of the corresponding untruncated Yangian isomorphism by the canonical quotient maps. This would quantize the multiplication isomorphism for generalized affine Grassmannian slices and is intended to express the local relationship between adjacent truncated shifted Yangians.