2010/02/25 by Indranil Biswas, I. Biswas, Biswas, I. +3
Mathematics · #14F05 #14L30 #14M17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14F05 #msc:14L30 #msc:14M17
paper · pdf · doi:10.48550/arxiv.1002.4821
5 pages. to appear in Intern. Journ. of Mathematics
arxiv created 2010/02/25 · openalex publication_date 2010/02/25 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.