Abstract
Let H be a connected semisimple linear algebraic group defined over C and X a compact connected Riemann surface of genus at least three. Let M' X (H) be the moduli space parametrising all topologically trivial stable principal H-bundles over X whose automorphism group coincides with the centre of H. It is a Zariski open dense subset of the moduli space of stable principal H-bundles. We prove that there is a universal principal H-bundle over X × M' X (H) if and only if H is an adjoint group (i.e., the centre of H is trivial).
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