Geodesic
Generating symplectic and Hermitian dual polar spaces over arbitrary fields nonisomorphic to \(\mathbb F_{2}\)
The electronic journal of combinatorics, Tome 14 (2007)
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Cooperstein proved that every finite symplectic dual polar space $DW(2n-1,q)$, $q \neq 2$, can be generated by ${2n \choose n} - {2n \choose n-2}$ points and that every finite Hermitian dual polar space $DH(2n-1,q^2)$, $q \neq 2$, can be generated by ${2n \choose n}$ 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.
DOI : 10.37236/972
Classification : 51A45, 51A50
Mots-clés : symplectic dual polar space, Hermitian dual polar space 
@article{10_37236_972,
     author = {Bart De Bruyn and Antonio Pasini},
     title = {Generating symplectic and {Hermitian} dual polar spaces over arbitrary fields nonisomorphic to \(\mathbb {F_{2}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/972},
     zbl = {1169.51004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/972/}
}
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Bart De Bruyn; Antonio Pasini. Generating symplectic and Hermitian dual polar spaces over arbitrary fields nonisomorphic to \(\mathbb F_{2}\). The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/972

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