Simplicity of stable principal sheaves |
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Authors: | Biswas, Indranil Gomez, Tomas L. |
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Affiliation: | School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005 India indranil@math.tifr.res.in |
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Abstract: | Let M be a compact connected Kähler manifold, and let Gbe a connected complex reductive linear algebraic group. Weprove that a principal G-sheaf on M admits an admissible Einstein–Hermitianconnection if and only if the principal G-sheaf is polystable.Using this it is shown that the holomorphic sections of theadjoint vector bundle of a stable principal G-sheaf on M aregiven by the center of the Lie algebra of G. The Bogomolov inequalityis shown to be valid for polystable principal G-sheaves. |
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