关于$π_{1}(\mathbb P^1-\mathcal R)$到紧半单群的同态
On homomorphisms of $π_{1}(\mathbb P^1-\mathcal R)$ into compact semisimple groups
摘要：
对有限子集$\mathcal R$，给出了$π_{1}(\mathbb P^1 - \mathcal R)$到紧半单群的{ \em不可约}同态存在的可验证准则，使得套索在标记点周围的象的共轭类是固定的.利用\cite{bs}中的一个定理，将这个问题归结为给出$\mathbb{P}^1_{\mathbb{C}}$上稳定$\mathcal G$ -torson存在性的可验证准则，其中$\mathcal{G} \to \mathbb{P}^1_\mathbb{C}$是一个Bruhat-Tits群方案.
英文摘要：
The aim of this paper is to give verifiable criteria for the existence of {\em irreducible} homomorphisms of $π_{1}(\mathbb P^1 - \mathcal R)$ into compact semisimple groups, for a finite subset $\mathcal R$ such that the conjugacy classes of the images of lassos around the marked points are fixed. By a theorem in \cite{bs}, this question reduces into one of giving verifiable criteria for the existence of stable $\mathcal G$-torsors on $\mathbb{P}^1_{\mathbb{C}}$, where $\mathcal{G} \to \mathbb{P}^1_\mathbb{C}$ is a a Bruhat-Tits group scheme.
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