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

Bart De Bruyn UGent (2009) Linear Algebra and its Applications. 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
2010-03-05 09:43:01
@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.