TY - JOUR
T1 - Holomorphic principal bundles over a compact Kähler manifold
AU - Anchouche, Boudjemaâ
AU - Azad, Hassan
AU - Biswas, Indranil
PY - 2000/1/15
Y1 - 2000/1/15
N2 - 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 EG is a holomorphic principal G-bundle over a compact connected Kähler manifold M, and EG is semistable (resp. polystable), then the principal H -bundle EG XG 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.
AB - 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 EG is a holomorphic principal G-bundle over a compact connected Kähler manifold M, and EG is semistable (resp. polystable), then the principal H -bundle EG XG 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.
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U2 - 10.1016/S0764-4442(00)00130-0
DO - 10.1016/S0764-4442(00)00130-0
M3 - Article
AN - SCOPUS:0034649913
SN - 0764-4442
VL - 330
SP - 109
EP - 114
JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
IS - 2
ER -