Cooperstein [6], [7] proved that every finite symplectic dual polar space DW (2n-1,q), q not equal 2, can be generated by ((2nn)(n))-((2n)(n-)) points and that every finite Hermitian dual polar space DH(2n-1,q(2)), q not equal 2, can be generated by ((2n)(n)) points. In the present paper, we show that these conclusions remain valid for symplectic and Hermitian dual polar spaces over in finite fields. A consequence of this is that every Grassmann-embedding of asymplectic or Hermitian dual polar space is absolutely universal if the (possibly infinite) underlying field has size at least 3.

DE BRUYN, B., & Pasini, A. (2007). Generating symplectic and hermitian dual polar spaces over arbitrary fields nonisomorphic to F2. ELECTRONIC JOURNAL OF COMBINATORICS, 14(1).

Generating symplectic and hermitian dual polar spaces over arbitrary fields nonisomorphic to F2

PASINI, ANTONIO
2007

Abstract

Cooperstein [6], [7] proved that every finite symplectic dual polar space DW (2n-1,q), q not equal 2, can be generated by ((2nn)(n))-((2n)(n-)) points and that every finite Hermitian dual polar space DH(2n-1,q(2)), q not equal 2, can be generated by ((2n)(n)) points. In the present paper, we show that these conclusions remain valid for symplectic and Hermitian dual polar spaces over in finite fields. A consequence of this is that every Grassmann-embedding of asymplectic or Hermitian dual polar space is absolutely universal if the (possibly infinite) underlying field has size at least 3.
DE BRUYN, B., & Pasini, A. (2007). Generating symplectic and hermitian dual polar spaces over arbitrary fields nonisomorphic to F2. ELECTRONIC JOURNAL OF COMBINATORICS, 14(1).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/7245
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