Strong stability of the homogeneous Levi bundle

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 1, Page 53--68.

Biswas, Indranil
Strong stability of the homogeneous Levi bundle
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Abstract:
Let $G$ be a connected semisimple linear algebraic group defined over an algebraically closed field. Let $P\,\subset\,G$ be a parabolic subgroup without any simple factor, and let $L(P)$ denote the Levi quotient of $P$. In this continuation of \cite{Bi}, we prove that the principal $L(P)$--bundle $(G\times L(P))/P$ over the homogeneous space $G/P$ is stable with respect to any polarization on $G/P$. When the characteristic of the base field is positive, this principal $L(P)$--bundle is shown to be strongly stable with respect to any polarization on $G/P$.

Keywords: Strongly stable bundle, homogeneous space, Levi quotient

Mathematics Subject Classification (2000): Primary 14L30; Secondary 14F05
Mathematical Reviews Number: MR2422589

Received: 2004-12-07