Abstract
It is known that semistable sheaves V admit a filtration whose quotients are stable and have the same slope of V , named the Jordan–Hölder filtration. We give the analogous result for principal Higgs bundles on curves. Let G be a reductive algebraic group over C , if E = ( E , ϕ ) is a semistable principal Higgs G -bundle, there exists a parabolic subgroup P of G and an admissible reduction of the structure group of E to that parabolic such that the principal Higgs bundle obtained by extending the structure group to the Levi factor L ( P ) of P is a stable principal Higgs bundle. The extension of the structure group L ( P ) to G of the latter stable principal bundle is the graded module gr ( E ) .
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