Criteria for existence of stable parahoric _n, _n and bundles on ^1 (original) (raw)

Let p: Y X be a Galois cover of smooth projective curves over with Galois group Γ. This paper is devoted to the study of principal orthogonal and symplectic bundles E on Y to which the action of Γ on Y lifts. We notably describe them intrinsically in terms of objects defined on X and call these objects parahoric bundles. We give necessary and sufficient conditions for the non-emptiness of the moduli of stable (and semi-stable) parahoric special orthogonal, symplectic and spin bundles on the projective line ^1.