A criterion for homogeneous principal bundles

Details A criterion for homogeneous principal bundles A criterion for homogeneous principal bundles

2010-02-25

arxiv.org/abs/1002.4821v1

Mathematics

Algebraic Geometry

5 pages. to appear in Intern. Journ. of Mathematics

Scientific paper

We consider principal bundles over homogeneous spaces G/P, where P is a parabolic subgroup of a semisimple and simply connected complex linear algebraic group G. We prove that a holomorphic principal H--bundle, where H is a complex reductive group, is homogeneous if the adjoint vector bundle ad(E) is homogeneous. We also show that E is homogeneous if its associated vector bundle for any finite dimensional faithful H--module is homogeneous.

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