Generating Symplectic and Hermitian Dual Polar Spaces over Arbitrary Fields Nonisomorphic to F2
نویسندگان
چکیده
Cooperstein [6], [7] proved that every finite symplectic dual polar space DW (2n− 1, q), q 6= 2, can be generated by ( 2n n ) − ( 2n n−2 ) points and that every finite Hermitian dual polar space DH(2n − 1, q2), q 6= 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 infinite fields. A consequence of this is that every Grassmann-embedding of a symplectic or Hermitian dual polar space is absolutely universal if the (possibly infinite) underlying field has size at least 3.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007