## Abstract

Let p : G → H be a homomorphism between connected reductive algebraic groups over ℂ such that the center of the Lie algebra g is sent to the center of h. If E_{G} is a holomorphic principal G-bundle over a compact connected Kähler manifold M, and E_{G} is semistable (resp. polystable), then the principal H -bundle E_{G} X_{G} H is also semistable (resp. polystable). A G-bundle over M is polystable if and only if it admits an Einstein-Hermitian connection; this is an analog of a theorem of Uhlenbeck and Yau for G-bundles. Two different formulations of the G-bundle analog of the Harder-Narasimhan reduction have been established. The equivalence of the two formulations is a consequence of a group theoretic result.

Original language | English |
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Pages (from-to) | 109-114 |

Number of pages | 6 |

Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |

Volume | 330 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 15 2000 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics