Moduli of parahoric G-torsors on a compact Riemann surface

Abstract

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