We show that the representation of a symplectic spread $cS$ of $PG(5,2^e)$ on the grassmannian of the planes of $PG(5,2^e)$ defines an ovoid of $Q^+(7,2^e)$ which, in turn, via triality defines a spread of $Q^+(7,2^e)$ one slice of which is isomorphic to $cS.$ This allows to explicitly compute the ovoid of $Q^+(7,2^e)$ without using a triality map. We conclude with some remarks on symplectic spreads and on some particular partial spreads of $Q^+(7,2^e)$ defined via the above representation by partial symplectic ovoids of $PG(3,2^e)$.
Some remarks on the Spin Module Representation of $Sp_6(2^e)$ / Bader, Laura; Lunardon, Guglielmo. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 339:(2016), pp. 1265-1273.
Some remarks on the Spin Module Representation of $Sp_6(2^e)$
BADER, LAURA;LUNARDON, GUGLIELMO
2016
Abstract
We show that the representation of a symplectic spread $cS$ of $PG(5,2^e)$ on the grassmannian of the planes of $PG(5,2^e)$ defines an ovoid of $Q^+(7,2^e)$ which, in turn, via triality defines a spread of $Q^+(7,2^e)$ one slice of which is isomorphic to $cS.$ This allows to explicitly compute the ovoid of $Q^+(7,2^e)$ without using a triality map. We conclude with some remarks on symplectic spreads and on some particular partial spreads of $Q^+(7,2^e)$ defined via the above representation by partial symplectic ovoids of $PG(3,2^e)$.File | Dimensione | Formato | |
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