On the nucleus of the Grassmann embedding of the symplectic dual polar space DSp(2n,F), char(F)=2

Authors:
Rieuwert J. Blok;Ilaria Cardinali;Bart De Bruyn
Affiliations:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA;Department of Information Engineering, University of Siena, I-53100 Siena, Italy;Department of Pure Mathematics and Computer Algebra, Ghent University, B-9000 Gent, Belgium
Venue:
European Journal of Combinatorics
Year:
2009

Citing 7
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Abstract

Let n=3 and let F be a field of characteristic 2. Let DSp(2n,F) denote the dual polar space associated with the building of type C"n over F and let G"n"-"2 denote the (n-2)-Grassmannian of type C"n. Using the bijective correspondence between the points of G"n"-"2 and the quads of DSp(2n,F), we construct a full projective embedding of G"n"-"2 into the nucleus of the Grassmann embedding of DSp(2n,F). This generalizes a result of an earlier paper [I. Cardinali, G. Lunardon, A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3, J. Combin. Theory Ser. A (in press)] which contains an alternative proof of this fact in the case when n=3 and F is finite.