Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 10, Number 3 (2003), 437-449.
Polarities of Symplectic Quadrangles
We give a simple proof of the known fact that the symplectic quadrangle is self-dual if and only if the ground field is perfect of characteristic~2, and that a polarity exists exactly if there is a root of the Frobenius automorphism. Moreover, we determine all polarities, characterize the conjugacy classes of polarities, and use the results to give a simple proof that the centralizer of any polarity acts two-transitively on the ovoid of absolute points. The proofs use elementary calculations in solvable subgroups of the symplectic group.
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 3 (2003), 437-449.
First available in Project Euclid: 12 September 2003
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Stroppel, Markus. Polarities of Symplectic Quadrangles. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 3, 437--449. https://projecteuclid.org/euclid.bbms/1063372348