On homomorphisms of $π_{1}(\mathbb P^1-\mathcal R)$ into compact semisimple groups

Abstract

The aim of this paper is to give verifiable criteria for the existence of irreducible homomorphisms of π 1 (P 1 − R) into compact semisimple groups, for a finite subset R such that the conjugacy classes of the images of lassos around the marked points are fixed. By a theorem in [2], this question reduces into one of giving verifiable criteria for the existence of stable G-torsors on P 1 C , where G → P 1C is a a Bruhat-Tits group scheme.