Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).
@article{bwmeta1.element.doi-10_2478_s11533-013-0330-9,
author = {Indranil Biswas and Andrei Teleman},
title = {Invariant connections and invariant holomorphic bundles on homogeneous manifolds},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1-13},
zbl = {1288.53040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0330-9}
}
Indranil Biswas; Andrei Teleman. Invariant connections and invariant holomorphic bundles on homogeneous manifolds. Open Mathematics, Tome 12 (2014) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0330-9/
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