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

(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:
http://hdl.handle.net/1854/LU-879154

- author
- Bart De Bruyn UGent
- organization
- year
- 2009
- 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.