This is related to the earlier question here

In Conjecture 25.4.2 in his "Introduction to Quantum Groups," Lusztig conjectures that "If the Cartan datum is symmetric, then the structure constants $m_{a,b}^c$, $\hat m_c^{a,b}$ are in $N[v,v^{-1}]$.

In what cases is this proven? I only care about classical groups, specifically split reductive groups over $Z$ as constructed via Lusztig's canonical bases (specialize at $v=1$). I would love it if the structure constants were non-negative, so that there were no troublesome signs floating around in the antipode. When is this known to be the case? My googling leads me to suspect something is known in the simply-laced case. Anything more general yet? References? I'm not interested in the non-symmetric case.