The quantum Q-system conjecture for Macdonald operators of types BCD

Let $G$ be one of the classical types $D_N$, $B_N$, or $C_N$, and let $M_{a,n}^{(G)}$ be the associated Macdonald difference operators, with the superscript $G$ omitted below. Let $\rho$ denote the commutation exponent appearing in the corresponding quantum Q-system. Quantum Q-system conjecture. The operators $M_{a,n}^{(G)}$ obey the renormalized quantum Q-system relations of types $D_N$, $B_N$, and $C_N$, namely the complete families of commutation and mutation relations displayed in the source. These relations have been checked numerically up to $N=6$ and are the main algebraic structure underlying the proposed difference-operator realization of the quantum Q-systems; a general proof remains open.