Invariant connections and invariant holomorphic bundles on homogeneous manifolds

Indranil Biswas 1  and Andrei Teleman 2
  • 1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400005, India
  • 2 CMI, LATP, Aix-Marseille Université, 39 Rue F. Joliot-Curie, 13453, Marseille Cedex 13, France

Abstract

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).

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