Understand
Let ${\mathfrak g}$ be a complex semisimple Lie algebra, and $Y_h({\mathfrak g})$, $U_q(L{\mathfrak g})$ the corresponding Yangian and quantum loop algebra, with deformation parameters related by $q=\exp(\pi i h)$.
- When $h$ is not a rational number, we constructed in arXiv:1310.7318 a faithful functor $\Gamma$ from the category of finite-dimensional representations of $Y_h ({\mathfrak g})$ to those of $U_q(L{\mathfrak g})$.
- The functor $\Gamma$ is governed by the additive difference equations defined by the commuting fields of the Yangian, and restricts to an equivalence on a subcategory of $Y_h({\mathfrak g})$ defined by choosing a branch of the logarithm.
- In this paper, we construct a tensor structure on $\Gamma$ and show that, if $|q|\neq 1$, it yields an equivalence of meromorphic braided tensor categories, when $Y_h({\mathfrak g})$ and $U_q(L{\mathfrak g})$ are endowed with the deformed Drinfeld coproducts and the commutative part of the universal $R$-matrix.