Shifted-quantum-affine-algebra factorization conjecture

Let $bpsi$ be the highest $l$-weight of an irreducible $l$-highest-weight module $L(bpsi)$ over the quantum affine Borel algebra $\mathcal{U}_qmathfrak{b}$. Let mu\frac{in P^{vee} be determined by the degree of $bpsi$, and let $L^{mu}(bpsi)$ be the irreducible $l$-highest-weight representation of the shifted quantum affine algebra $U_q^{mu}$. Shifted-algebra factorization conjecture. The $q$-character factors as

$$\chi_q(L(bpsi))=c\times a,$$

where

c=\prod_{\alpha\frac{inDelta_+}\left(\frac{1}{1-e^{-\alpha}}\right)^{\max(0,\alpha(mu))}

and

$$a=\chi_q(L^{mu}(bpsi)).$$

The source proposes this as an explanation, via shifted quantum affine algebras, of the factorization of q-characters into constant and non-constant parts; it does not establish the assertion.