Abstract:
Reflection equations, arsing from quantum integrable systems with boundary conditions, are the analog of Yang-Baxter equations on a half line. Geometrically, they encode the cylinder braid groups. Algebraically they are closely related to quantum homogenous spaces. In this talk, we first give an introduction to the Stokes phenomenon of an ODE with irregular singularities. We then prove that the Stokes matrices of cyclotomic Knizhnik–Zamolodchikov (KZ) equations give universal solutions to reflection equations. As an application, we show that the isomonodromy deformation of the KZ equations is a quantization of the Dubrovin connections of Frobenius manifolds from various aspects.
