Polarities of Symplectic Quadrangles

Stroppel, Markus

Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 437-449 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2003-09-14
Classification:  generalized quadrangle,  symplectic quadrangle,  polarity,  duality,  ovoid,  elation generalized quadrangle,  translation generalized quadrangle,  symplectic group,  51E12,  51A10,  51A50