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Base subsets in symplectic Grassmannians of small indices

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Let V and V′ be n-dimensional vector spaces. Let also Ω and Ω′ be non-degenerate symplectic forms defined on V and V′, respectively. Denote by Π and Π′ the projective spaces associated with V and V′. We put for the sets of k-dimensional totally isotropic subspaces of Π and Π′. We study mappings of BF03322901 which transfer base subsets to base subsets and show that such mappings are induced by strong embeddings of Π to Π′ if 3k + 3 ≤ n.

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References

  1. Benz W., Geometrische Transformationen. B.I. Wissenschaftsverlag, Mannheim Leipzig Wien Zürich, 1992.

  2. Chow W. L., On the geometry of algebraic homogeneous spaces, Ann. of Math. 50 (1949) 32–67.

    Article  MathSciNet  MATH  Google Scholar 

  3. Dieudonné J., La Géométrie des Groupes Classiques, 3rd ed., Springer, Berlin Heidelberg New York, 1971.

    MATH  Google Scholar 

  4. Faure C. A., Frölicher A., Morphisms of Projective Geometries and Semilinear maps, Geom. Dedicata, 53 (1994), 237–262.

    Article  MathSciNet  MATH  Google Scholar 

  5. Havlicek H., A Generalization of Brauner’s Theorem on Linear Mappings, Mitt. Math. Sem. Univ. Gieβen, 215 (1994), 27–41.

    MathSciNet  MATH  Google Scholar 

  6. Huang W.-L, Kreuzer A., Basis preserving maps of linear spaces, Arch. Math. (Basel) 64(1995), 6, 530–533.

    Article  MathSciNet  MATH  Google Scholar 

  7. Huang W.-L, Adjacency preserving mappings of invariant subspaces of a null system, Proc. A.M.S. 128, N8 (2000), 2451–2455.

    Article  MATH  Google Scholar 

  8. Huang W.-L, Characterization of the transformation group of the space of a Null System, Results Math. 40 (2001), 226–232.

    MathSciNet  MATH  Google Scholar 

  9. Pankov M., A characterization of geometrical mappings of Grassmann spaces, Results Math. 45(2004), 319–327.

    MathSciNet  MATH  Google Scholar 

  10. Pankov M., Mappings of the sets of invariant subspaces of null systems, Beiträge Algebra Geom., 45(2004), 389–399.

    MathSciNet  MATH  Google Scholar 

  11. Pankov M., Base preserving maps in symplectic geometry, submitted to Abh. Math. Sem. Univ. Hamburg.

  12. Pankov M., Prazmovski K., Żynel M., Geometry of polar Grassmann spaces, submitted to Demonstratio Math.

  13. Tits J., Buildings spherical types and finite BN-pairs, Lect. Notes Math. 386, Springer-Verlag, 1974.

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  1. Institute of Mathematics National Academy of Science of Ukraine, Tereshchenkivska 3, Kiev 01601, Ukraine

    Mark Pankov

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  1. Mark Pankov
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Correspondence to Mark Pankov.

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Pankov, M. Base subsets in symplectic Grassmannians of small indices. Results. Math. 48, 124–130 (2005). https://doi.org/10.1007/BF03322901

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