On the stability of homogeneous vector bundles
Vol. 11 (2004), No. 2, Page 133--140.
Biswas, Indranil
On the stability of homogeneous vector bundles
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Abstract:
Let G be a connected semisimple linear algebraic group over an algebraically closed field k and P⊂G a parabolic subgroup without any simple factor. Let V be an irreducible P--module and EP(V)=(G×V)/P the associated vector bundle over G/P. We prove that EP(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.
Keywords: Homogeneous bundle, parabolic subgroup, stability
Mathematics Subject Classification (2000): 14L30, 14F05, 14M17.
Mathematical Reviews Number: MR2081423
Received: 2003-12-09
