  Starting with a four-dimensional gauge theory approach to rational, elliptic,
and trigonometric solutions of the Yang-Baxter equation, we determine the
corresponding quantum group deformations to all orders in $\hbar$ by deducing
their RTT presentations. The arguments we give are a mix of familiar ones with
reasoning that is more transparent from the four-dimensional gauge theory point
of view. The arguments apply most directly for $\mathfrak{gl}_N$ and can be
extended to all simple Lie algebras other than $\mathfrak{e}_8$ by taking into
account the self-duality of some representations, the framing anomaly for
Wilson operators, and the existence of quantum vertices at which several Wilson
operators can end.
