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Home > Vol 30, No 4 (2009)

Bart De Bruyn

Let \mathbb K {\mathbb{K}} be a perfect field of characteristic 2. In this paper, we classify all hyperplanes of the symplectic dual polar space DW(5,\mathbb K) DW(5,{\mathbb{K}}) that arise from its Grassmann embedding. We show that the number of isomorphism classes of such hyperplanes is equal to 5+ N, where N is the number of equivalence classes of the following equivalence relation R on the set { l Ĩ \mathbb K  |  X ²+ l X+1 isirreducible \{λ\in {\mathbb{K}}\,|\,X^{2}+λX+1\mbox{ isirreducible} in \mathbb K[ X]} \mbox{in }{\mathbb{K}}[X]\} : ( λ  ₁, λ  ₂)\in  R whenever there exists an automorphism σ  of \mathbb K {\mathbb{K}} and an a Ĩ \mathbb K a\in {\mathbb{K}} such that ( λ  ₂ ^σ  )  ^- 1= λ  ₁  ^- 1+ a ²+ a.

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