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

AbstractLet 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 EP(H) = (G × H)/P over G/P. We prove that EP (H) is strongly stable with respect to any polarization on G/P