On isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces

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• 作者：Bart De Bruyn
• 关键词：Symplectic/Hermitian dual polar space ; Grassmann-embedding ; Hyperplane
• 刊名：Linear Algebra and its Applications
• 出版年：2009
• 出版时间：15 April 2009
• 年：2009
• 卷：430
• 期：8-9
• 页码：2541-2552
• 全文大小：192 K

文摘

Let n2, let be fields such that is a quadratic Galois-extension of and let θ denote the unique nontrivial element in . Suppose the symplectic dual polar space is fully and isometrically embedded into the Hermitian dual polar space . We prove that the projective embedding of induced by the Grassmann-embedding of is isomorphic to the Grassmann-embedding of . We also prove that if n is even, then the set of points of at distance at most from is a hyperplane of which arises from the Grassmann-embedding of .