Journal of the Ramanujan Mathematical Society

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Orthogonal and Symplectic Grassmannians of Division Algebras


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1 Universite Pierre et Marie Curie, Institute de Mathematiques de Jussieu, Paris, France
     

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We consider a central division algebra (over a field) endowed with a quadratic pair or with a symplectic involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. This covers a recent conjecture raised by M. Zhykhovich. The remaining related projective homogeneous varieties are 2-compressible in general.
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  • Orthogonal and Symplectic Grassmannians of Division Algebras

Abstract Views: 185  |  PDF Views: 0

Authors

Nikita A. Karpenko
Universite Pierre et Marie Curie, Institute de Mathematiques de Jussieu, Paris, France

Abstract


We consider a central division algebra (over a field) endowed with a quadratic pair or with a symplectic involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. This covers a recent conjecture raised by M. Zhykhovich. The remaining related projective homogeneous varieties are 2-compressible in general.