Criteria for existence of stable parahoric SOn, Spn and Spin bundles on P1

Let p : Y -> X be a Galois cover of smooth projective curves over C with Galois group F. This paper is devoted to the study of principal orthogonal and symplectic bundles E on Y to which the action of Gamma 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 P-l.