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

Bart De Bruyn UGent (2009) 430. p.2541-2552
abstract
Let \geq 2$, let ,K'$ be fields such that '$is a quadratic Galois-extension of$ and let $\theta$ denote the unique nontrivial element in (K'/K)$. Suppose the symplectic dual polar space (2n-1,K)$ is fully and isometrically embedded into the Hermitian dual polar space (2n-1,K',\theta)$. We prove that the projective embedding of (2n-1,K)$ induced by the Grassmann-embedding of (2n-1,K',\theta)$is isomorphic to the Grassmann-embedding of (2n-1,K)$. We also prove that if $is even, then the set of points of (2n-1,K',\theta)$ at distance at most $\frac{n}{2}-1$ from (2n-1,K)$is a hyperplane of (2n-1,K',\theta)$ which arises from the Grassmann-embedding of (2n-1,K',\theta)$. Please use this url to cite or link to this publication: author organization year type journalArticle (original) publication status published subject keyword symplectic/Hermitian dual polar space, hyperplane, Grassmann-embedding journal title Linear Algebra and its Applications Linear Algebra Appl. volume 430 pages 2541 - 2552 Web of Science type Article Web of Science id 000264864400051 JCR category MATHEMATICS, APPLIED JCR impact factor 1.073 (2009) JCR rank 65/202 (2009) JCR quartile 2 (2009) ISSN 0024-3795 DOI 10.1016/j.laa.2008.12.025 language English UGent publication? yes classification A1 copyright statement I don't know the status of the copyright for this publication id 879154 handle http://hdl.handle.net/1854/LU-879154 date created 2010-02-24 14:32:43 date last changed 2016-12-19 15:40:48 @article{879154, abstract = {Let {\textbackslash}geq 2\$, let ,K'\$be fields such that '\$ is a quadratic Galois-extension of \$and let \${\textbackslash}theta\$denote the unique nontrivial element in (K'/K)\$. Suppose the symplectic dual polar space (2n-1,K)\$is fully and isometrically embedded into the Hermitian dual polar space (2n-1,K',{\textbackslash}theta)\$. We prove that the projective embedding
of (2n-1,K)\$induced by the Grassmann-embedding of (2n-1,K',{\textbackslash}theta)\$ is isomorphic to the Grassmann-embedding of (2n-1,K)\$. We also prove that if \$ is even, then the set of points of (2n-1,K',{\textbackslash}theta)\$at distance at most \${\textbackslash}frac\{n\}\{2\}-1\$from (2n-1,K)\$ is a hyperplane of (2n-1,K',{\textbackslash}theta)\$which arises from the Grassmann-embedding of (2n-1,K',{\textbackslash}theta)\$.},
author       = {De Bruyn, Bart},
issn         = {0024-3795},
journal      = {Linear Algebra and its Applications},
keyword      = {symplectic/Hermitian dual polar space,hyperplane,Grassmann-embedding},
language     = {eng},
pages        = {2541--2552},
title        = {On isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces.},
url          = {http://dx.doi.org/10.1016/j.laa.2008.12.025},
volume       = {430},
year         = {2009},
}


Chicago
De Bruyn, Bart. 2009. “On Isometric Full Embeddings of Symplectic Dual Polar Spaces into Hermitian Dual Polar Spaces.” Linear Algebra and Its Applications 430: 2541–2552.
APA
De Bruyn, B. (2009). On isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces. Linear Algebra and its Applications, 430, 2541–2552.
Vancouver
1.
De Bruyn B. On isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces. Linear Algebra and its Applications. 2009;430:2541–52.
MLA
De Bruyn, Bart. “On Isometric Full Embeddings of Symplectic Dual Polar Spaces into Hermitian Dual Polar Spaces.” Linear Algebra and its Applications 430 (2009): 2541–2552. Print.