Irreducible representations of knot groups into SL(n,C)

TL;DR

This paper investigates the existence and deformation of certain reducible and metabelian representations of knot groups into SL(n,C), extending previous studies to identify conditions for irreducible deformations.

Contribution

It introduces new conditions under which reducible metabelian representations of knot groups into SL(n,C) can be deformed into irreducible representations.

Findings

Existence of irreducible deformations under specific hypotheses

Extension of previous representation studies to higher dimensions

Conditions for deformability of knot group representations

Abstract

The aim of this article is to study the existence of certain reducible, metabelian representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$ which generalise the representations studied previously by G.~Burde and G.~de Rham. Under specific hypotheses we prove the existence of irreducible deformations of such representations of knot groups into $\mathrm{SL}(n,\mathbf{C})$.