Generating Symplectic and Hermitian Dual Polar Spaces over Arbitrary Fields Nonisomorphic to F2

@article{Bruyn2007GeneratingSA,
  title={Generating Symplectic and Hermitian Dual Polar Spaces over Arbitrary Fields Nonisomorphic to F2},
  author={Bart De Bruyn and Antonio Pasini},
  journal={Electr. J. Comb.},
  year={2007},
  volume={14}
}
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… CONTINUE READING