Abstract
Let be a connected complex reductive linear algebraic group, and let be a maximal compact subgroup. The Lie algebra of is denoted by . A holomorphic Hermitian principal -bundle is a pair of the form , where is a holomorphic principal -bundle and is a -reduction of structure group to . Two holomorphic Hermitian principal -bundles and are called holomorphically isometric if there is a holomorphic isomorphism of the principal -bundle with which takes to . We consider all holomorphic Hermitian principal -bundles over the upper half-plane such that the pullback of by each holomorphic automorphism of is holomorphically isometric to itself. We prove that the isomorphism classes of such pairs are parameterized by the equivalence classes of pairs of the form , where is a homomorphism, and such that . (Here is the homomorphism of Lie algebras associated to .) Two such pairs and are called equivalent if there is an element such that and .
Citation
Indranil Biswas. "Homogeneous principal bundles over the upper half-plane." Kyoto J. Math. 50 (2) 325 - 363, Summer 2010. https://doi.org/10.1215/0023608X-2009-016
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