Stokes phenomena, Poisson-Lie groups and quantum groups

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.