Embeddings and hyperplanes of discrete geometries
European Journal of Combinatorics
On the generation of dual polar spaces of unitary type over finite fields
European Journal of Combinatorics
On the generation of dual polar spaces of symplectic type over finite fields
Journal of Combinatorial Theory Series A
Valuations and hyperplanes of dual polar spaces
Journal of Combinatorial Theory Series A
Minimal full polarized embeddings of dual polar spaces
Journal of Algebraic Combinatorics: An International Journal
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Let @D be a thick dual polar space and F a convex subspace of diameter at least 2 of @D. Every hyperplane G of the subgeometry F@? of @D induced on F will give rise to a hyperplane H of @D, the so-called extension of G. We show that F and G are in some sense uniquely determined by H. We also consider the following problem: if e is a full projective embedding of @D and if e"F is the full embedding of F@? induced by e, does the fact that G arises from the embedding e"F imply that H arises from the embedding e? We will study this problem in the cases that e is an absolutely universal embedding, a minimal full polarized embedding or a Grassmann embedding of a symplectic dual polar space. Our study will allow us to prove that if e is absolutely universal, then also e"F is absolutely universal.