## On the stability of homogeneous vector bundles

J. Math. Sci. Univ. Tokyo
Vol. 11 (2004), No. 2, Page 133--140.

Biswas, Indranil
On the stability of homogeneous vector bundles
Let $G$ be a connected semisimple linear algebraic group over an algebraically closed field $k$ and $P\, \subset\, G$ a parabolic subgroup without any simple factor. Let $V$ be an irreducible $P$--module and $E_P(V) = (G\times V)/P$ the associated vector bundle over $G/P$. We prove that $E_P(V)$ is stable with respect to any polarization on $G/P$. In \cite{Um} this was proved under the assumption that the characteristic of $k$ is zero and the question was asked whether it remains valid when the characteristic is positive.