The generic quantum group Drinfeld center conjecture

Let $\mathfrak g$ be a semisimple Lie algebra with weight and root lattices $P$ and $Q$, respectively. For $q\in\mathbb{C}$, let $U_q(\mathfrak g)\mathbf{-mod}$ be the category of finite-dimensional type-I representations, and let $\mathcal{Z}(U_q(\mathfrak g)\mathbf{-mod})$ be its Drinfeld center. The category has a canonical functor

$$Z:\left(U_q(\mathfrak g)\mathbf{-mod}\boxtimes U_q(\mathfrak g)\mathbf{-mod}^{\mathrm{rev}}\boxtimes\operatorname{Rep}(P/Q)\right)^\gamma\to\mathcal{Z}(U_q(\mathfrak g)\mathbf{-mod}),$$

where $\gamma$ is a bicharacter of $(P/Q)^{\oplus 3}$. Generic quantum group Drinfeld center conjecture. There exists such a bicharacter $\gamma$ for which $Z$ is an equivalence of braided tensor categories whenever $q\in\mathbb{C}$ is not a root of unity. The conjecture predicts an explicit description of the Drinfeld center in the generic, non-root-of-unity case; no resolution is supplied in the source.