Two new classes of hyperplanes of the dual polar space DH

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• 作者：Bart De Bruyn
• 关键词：Hermitian dual polar space ; Hyperplane ; Grassmann embedding ; Universal embedding ; Symplectic polar space ; Hyperbolic line
• 刊名：Linear Algebra and its Applications
• 出版年：2008
• 出版时间：16 October 2008
• 年：2008
• 卷：429
• 期：8-9
• 页码：2030-2045
• 全文大小：230 K

文摘

Let Γ_n(q) denote the geometry of the hyperbolic lines of the symplectic polar space W(2n-1,q),n2. We show that every hyperplane of Γ_n(q) gives rise to a hyperplane of the Hermitian dual polar space DH(2n-1,q²). In this way we obtain two new classes of hyperplanes of DH(2n-1,4) which do not arise from the Grassmann embedding of DH(2n-1,4).