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
The hyperplanes of DQ(2n,K) and DQ-(2n+1,q) which arise from their spin-embeddings
Journal of Combinatorial Theory Series A
The structure of the spin-embeddings of dual polar spaces and related geometries
European Journal of Combinatorics
Note: A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3
Journal of Combinatorial Theory Series A
On the nucleus of the Grassmann embedding of the symplectic dual polar space DSp(2n,F), char(F)=2
European Journal of Combinatorics
Hyperplanes of $DW(5,{\mathbb{K}})$ with ${\mathbb{K}}$ a perfect field of characteristic 2
Journal of Algebraic Combinatorics: An International Journal
Polarized and homogeneous embeddings of dual polar spaces
Journal of Algebraic Combinatorics: An International Journal
On extensions of hyperplanes of dual polar spaces
Journal of Combinatorial Theory Series A
Highest weight modules and polarized embeddings of shadow spaces
Journal of Algebraic Combinatorics: An International Journal
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Let 驴 be a thick dual polar space of rank n 驴 2 admitting a full polarized embedding e in a finite-dimensional projective space 驴, i.e., for every point x of 驴, e maps the set of points of 驴 at non-maximal distance from x into a hyperplane e驴(x) of 驴. Using a result of Kasikova and Shult [11], we are able the show that there exists up to isomorphisms a unique full polarized embedding of 驴 of minimal dimension. We also show that e驴 realizes a full polarized embedding of 驴 into a subspace of the dual of 驴, and that e驴 is isomorphic to the minimal full polarized embedding of 驴. In the final section, we will determine the minimal full polarized embeddings of the finite dual polar spaces DQ(2n,q), DQ 驴(2n+1,q), DH(2n驴1,q 2) and DW(2n驴1,q) (q odd), but the latter only for n驴 5. We shall prove that the minimal full polarized embeddings of DQ(2n,q), DQ 驴(2n+1,q) and DH(2n驴1,q 2) are the `natural' ones, whereas this is not always the case for DW(2n驴1, q).