A criterion for homogeneous principal bundles
Algebraic Geometry
2010-02-26 v1
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.
Cite
@article{arxiv.1002.4821,
title = {A criterion for homogeneous principal bundles},
author = {I. Biswas and G. Trautmann},
journal= {arXiv preprint arXiv:1002.4821},
year = {2010}
}
Comments
5 pages. to appear in Intern. Journ. of Mathematics