Stability of the tangent bundle of G/P in positive characteristics

Abstract

Let $G$ be an almost simple simply-connected affine algebraic group over an algebraically closed field $k$ of characteristic $p>0$. If $G$ has type $B_n$, $C_n$ or $F_4$, we assume that $p>2$, and if $G$ has type $G_2$, we assume that $p>3$. Let $P\subset G$ be a parabolic subgroup. We prove that the tangent bundle of $G/P$ is Frobenius stable with respect to the anticanonical polarization on $G/P$.