%0 Journal Article
%T A criterion for homogeneous principal bundles
%A I. Biswas
%A G. Trautmann
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1002.4821v1