Workshop on Representation Theory and Geometry

Let $G$ be a complex reductive group, $G^*$ its dual Poisson-Lie group, and $g$ the Lie algebra of $G$. $G$-valued Stokes phenomena were exploited by P. Boalch to linearise the Poisson structure on $G^*$. I will explain how $Ug$-valued Stokes phenomena can be used to give a purely transcendental construction of the quantum group $Uhg$, and show that the semiclassical limit of this construction recovers Boalch’s. The latter result is joint work with Xiaomeng Xu.