The pole-location conjecture for normalized R-matrices

Let $I_0$ index the fundamental representations, let $R^{{\operatorname{nor}}}_{ij}(x,y)$ be the normalized $R$-matrix for $i,j\in I_0$, and let $\gamma$ be the parameter defined in the source. Pole-location conjecture. Every pole of $R^{{\operatorname{nor}}}_{ij}(x,y)$ has the form $y/x=\pm q^n$ for some $n\in\gamma^{-1}\mathbb Z$ satisfying $0<n\leq(\delta,\rho)$, except in type $D_4^{(3)}$; in that case a third root of unity occurs in the coefficients. The claim is verified in the appendix for types $A_n^{(1)}$ and $C_n^{(1)}$, but remains conjectural in general.