The graded-character conjecture for KR-modules of types BCD

Let $I$ be the set of Dynkin labels, let $I_<\subset I$ be the labels of the short roots in types $B_N$ and $C_N$, and let $t_a=2$ for $a\in I_<$ and $t_a=1$ otherwise. Let $M_{a,k}^{(G)}$ be the difference operators of type $G\in\{B_N,C_N,D_N\}$, let $\mathbf n=(n_{a,i})$ encode the tensor product of Kirillov–Reshetikhin modules, and let $Q^{(G)}(\mathbf n)$ be the quadratic form displayed in the source. Graded-character conjecture. The graded characters of tensor products of KR-modules of types $BCD$ are given by the iterated action of the difference operators on the polynomial $1$, with the normalization and ordered product specified by the source formula. This conjecture depends on the quantum Q-system conjecture and would provide a difference-operator realization of graded KR-module characters; no resolution is stated in the supplied text.