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

## TL;DR

This paper explores the local relations of Wilson line junctions in refined SU(N) Chern-Simons theory, revealing a one-parameter deformation of quantum groups related to symmetric and antisymmetric representations.

## Contribution

It introduces local relations for Wilson line junctions that realize one-parameter deformations of quantum groups $ ext{U}_q( ext{sl}_m)$ and $ ext{U}_q( ext{sl}_{n|m})$, advancing understanding of refined Chern-Simons theory.

## Key findings

- Proposes local relations for Wilson line junctions in refined SU(N) Chern-Simons theory.
- Realizes one-parameter deformations of quantum groups $ ext{U}_q( ext{sl}_m)$ and $ ext{U}_q( ext{sl}_{n|m})$.
- Connects Wilson line junctions with algebraic deformations 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 $\dot{U}_{q}(\mathfrak{sl}_{n|m})$.