Stability of homogeneous principal bundles with a classical groupas the structure group

Abstract

Let G be a connected semisimple linear algebraic group defined over an algebraically closed field k and P ⊂ G a parabolic subgroup without any simple factor. Let H be a connected reductive linear algebraic group defined over the field k such that all the simple quotients of H are of classical type. Take any homomorphism π : P → H such that the image of p is not contained in any proper parabolic subgroup of H. Consider the corresponding principal H-bundle E P ( H) = ( G × H)/ P over G/ P. We prove that E P ( H) is strongly stable with respect to any polarization on G/ P.