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{\bf Bart De Bruyn and Antonio Pasini}
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{\bf Generating Symplectic and Hermitian Dual Polar Spaces over Arbitrary Fields Nonisomorphic to ${\Bbb F}_2$}
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Cooperstein proved that every finite symplectic dual polar space
$DW(2n-1,q)$, $q \not= 2$, can be generated by ${2n \choose n} - {2n
\choose n-2}$ points and that every finite Hermitian dual polar space
$DH(2n-1,q^2)$, $q \not= 2$, 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.
\bye