On irreducible representations of Fuchsian groups

Let R ⊂ P¹C be a finite subset of markings. Let G be an almost simple simply-connected algebraic group over C . Let KG denote the compact real form of G . Suppose for each lasso l around the marked point, a conjugacy class Cₗ in KG is prescribed. The aim of this paper is to give verifiable criteria for the existence of an irreducible homomorphism of π ₁( P¹C \,\, R) into KG such that the image of l lies in Cₗ .