A criterion for homogeneous principal bundles

Abstract

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.

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

References in corpus (1)

• Triviality of vector bundles on sufficiently twisted ind-Grassmannians

Cited by in corpus (1)

• Homogeneous bundles over abelian varieties