Junctions of refined Wilson lines and one-parameter deformation of quantum groups

Abstract

We study junctions of Wilson lines in refined SU(N) Chern-Simons theory and their local relations. We focus on junctions of Wilson lines in antisymmetric and symmetric powers of the fundamental representation and propose a set of local relations which realize one-parameter deformations of quantum groups $\dot{U}_{q}(\mathfrak{sl}_{m})$ and $\dot{U}_{q}(\mathfrak{sl}_{n|m})$.