Irreducible Representations of Knot Groups into $\mathrm{SL}(n,\mathbf{C})$

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 generalize 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 $\mathrm{SL}(n,\mathbf{C})$.