On holomorphic principal bundles over a compact Riemann surface admitting a flat connection. (English summary) Math. Ann. 322 (2002), no. 2, 333–346. Let G be a connected reductive linear algebraic group over C. Given a Levi factor L ⊂ G of some parabolic subgroup of G, let L0 = L/[L, L] denote its maximal abelian quotient. The main result in the paper under review is that a holomorphic principal G-bundle EG over a compact connected Riemann surface X admits a flat connection compatible with the holomorphic structure if and only if, for every Levi factor L and every reduction EL ⊂ EG of the structure group, the associated L0-bundle is topologically trivial over X. This generalizes a well-known result of A. Weil for holomorphic vector bundles over X (i.e. the case G = GL(n, C))
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