Moduli of parahoric 𝒢-torsors on a compact Riemann surface

Abstract

Let X X be an irreducible smooth projective algebraic curve of genus g ≥ 2 g \geq 2 over the ground field C \mathbb {C} , and let G G be a semisimple simply connected algebraic group. The aim of this paper is to introduce the notion of semistable and stable parahoric torsors under a certain Bruhat–Tits group scheme G \mathcal G and to construct the moduli space of semistable parahoric G \mathcal G -torsors; we also identify the underlying topological space of this moduli space with certain spaces of homomorphisms of Fuchsian groups into a maximal compact subgroup of G G . The results give a generalization of the earlier results of Mehta and Seshadri on parabolic vector bundles.