Factoriality conjecture for character varieties of free groups

Let $F_g$ be the free group of rank $g$, let $G$ be a reductive group, and let $DG$ denote its derived subgroup. Write $\mathcal{X}(F_g,G)$ for the character variety of representations of $F_g$ into $G$. Factoriality conjecture. The character variety $\mathcal{X}(F_g,G)$ is factorial if and only if $DG$ is simply connected. This conjecture proposes that simple connectivity of the derived subgroup exactly characterizes factoriality for these character varieties; the supplied source does not state a resolution.