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September 2003 Polarities of Symplectic Quadrangles
Markus Stroppel
Bull. Belg. Math. Soc. Simon Stevin 10(3): 437-449 (September 2003). DOI: 10.36045/bbms/1063372348

Abstract

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.

Citation

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Markus Stroppel. "Polarities of Symplectic Quadrangles." Bull. Belg. Math. Soc. Simon Stevin 10 (3) 437 - 449, September 2003. https://doi.org/10.36045/bbms/1063372348

Information

Published: September 2003
First available in Project Euclid: 12 September 2003

zbMATH: 1040.51005
MathSciNet: MR2017454
Digital Object Identifier: 10.36045/bbms/1063372348

Subjects:
Primary: 51A10, 51A50, 51E12

Rights: Copyright © 2003 The Belgian Mathematical Society

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Vol.10 • No. 3 • September 2003
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