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Algebras and Representation Theory

, Volume 22, Issue 1, pp 239–247 | Cite as

Stability of the Tangent Bundle of G/P in Positive Characteristics

  • Indranil BiswasEmail author
  • Pierre-Emmanuel Chaput
  • Christophe Mourougane
Article

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 Bn, Cn or F4, we assume that p >  2, and if G has type G2, we assume that p >  3. Let PG 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.

Keywords

Rational homogeneous space Tangent bundle Stability Frobenius 

Mathematics Subject Classification (2010)

14M17 14G17 14J60 

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Notes

Acknowledgements

We are very grateful to G. Ottaviani for pointing out an error in a previous version. He also brought [4] 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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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Indranil Biswas
    • 1
    Email author
  • Pierre-Emmanuel Chaput
    • 2
  • Christophe Mourougane
    • 3
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia
  2. 2.Domaine Scientifique Victor Grignard, 239, Boulevard des AiguillettesUniversité Henri Poincaré Nancy 1Vandoeuvre-lès-Nancy CédexFrance
  3. 3.Département de Mathématiques, Campus de Beaulieu, bât. 22-23Université de Rennes 1Rennes CédexFrance

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