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On irreducible representations of Fuchsian groups
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 27 August 2024, pp. 1-21
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Let
${\mathcal {R}} \subset \mathbb {P}^1_{\mathbb {C}}$ be a finite subset of markings. Let G be an almost simple simply-connected algebraic group over 
$\mathbb {C}$. Let 
$K_G$ denote the compact real form of G. Suppose for each lasso l around the marked point, a conjugacy class 
$C_l$ in 
$K_G$ is prescribed. The aim of this paper is to give verifiable criteria for the existence of an irreducible homomorphism of 
$\pi _{1}(\mathbb P^1_{\mathbb {C}} \,{\backslash}\, {\mathcal {R}})$ into 
$K_G$ such that the image of l lies in 
$C_l$.
