Stability of the Tangent Bundle of G/P in Positive Characteristics
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 Bn, Cn or F4, we assume that p > 2, and if G has type G2, we assume that p > 3. Let P ⊂ 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.
KeywordsRational homogeneous space Tangent bundle Stability Frobenius
Mathematics Subject Classification (2010)14M17 14G17 14J60
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We are very grateful to G. Ottaviani for pointing out an error in a previous version. He also brought  to our attention. The second and third authors thank the Tata Institute of Fundamental Research, while the first author thanks Institut de Mathématiques de Jussieu for hospitality during various stages of this work.
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