Base subsets of symplectic Grassmannians |
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Authors: | Mark Pankov |
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Affiliation: | (1) Department of Mathematics and Information Technology, University of Warmia and Mazury, Żolnierska 14A, 10-561 Olsztyn, Poland |
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Abstract: | Let V and V′ be 2n-dimensional vector spaces over fields F and F′. Let also Ω: V× V→ F and Ω′: V′× V′→ F′ be non-degenerate symplectic forms. Denote by Π and Π′ the associated (2n−1)-dimensional projective spaces. The sets of k-dimensional totally isotropic subspaces of Π and Π′ will be denoted by and ${mathcal G}'_{k}$, respectively. Apartments of the associated buildings intersect and by so-called base subsets. We show that every mapping of to sending base subsets to base subsets is induced by a symplectic embedding of Π to Π′. |
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Keywords: | Tits building Symplectic Grassmannians Base subsets |
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