### A property of isometric mappings between dual polar spaces of type DQ(2n,K)

Bart De Bruyn UGent (2010) 14(3). p.307-318
abstract
Let f be an isometric embedding of the dual polar space Delta = DQ(2n, K) into Delta' = DQ(2n, K'). Let P denote the point-set of Delta and let e' : Delta' -> Sigma' congruent to PG(2(n) - 1, K') denote the spin-embedding of Delta'. We show that for every locally singular hyperplane H of Delta, there exists a unique locally singular hyperplane H' of Delta' such that f(H) = f(P) boolean AND H'. We use this to show that there exists a subgeometry Sigma congruent to PG(2(n) - 1, K) of Sigma' such that: (i) e' circle f (x) is an element of Sigma for every point x of Delta; (ii) e := e' circle f defines a full embedding of Delta into Sigma, which is isomorphic to the spin-embedding of Delta.
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
dual polar space, isometric embedding, hyperplane, spin-embedding, SPIN-EMBEDDINGS, HYPERPLANES
journal title
ANNALS OF COMBINATORICS
Ann. Comb.
volume
14
issue
3
pages
307 - 318
Web of Science type
Article
Web of Science id
000292037400002
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.462 (2010)
JCR rank
186/235 (2010)
JCR quartile
4 (2010)
ISSN
0218-0006
DOI
10.1007/s00026-010-0061-6
language
English
UGent publication?
yes
classification
A1
I have transferred the copyright for this publication to the publisher
id
1108477
handle
http://hdl.handle.net/1854/LU-1108477
date created
2011-01-22 10:15:23
date last changed
2011-07-15 15:53:37
```@article{1108477,
abstract     = {Let f be an isometric embedding of the dual polar space Delta = DQ(2n, K) into Delta' = DQ(2n, K'). Let P denote the point-set of Delta and let e' : Delta' -{\textrangle} Sigma' congruent to PG(2(n) - 1, K') denote the spin-embedding of Delta'. We show that for every locally singular hyperplane H of Delta, there exists a unique locally singular hyperplane H' of Delta' such that f(H) = f(P) boolean AND H'. We use this to show that there exists a subgeometry Sigma congruent to PG(2(n) - 1, K) of Sigma' such that: (i) e' circle f (x) is an element of Sigma for every point x of Delta; (ii) e := e' circle f defines a full embedding of Delta into Sigma, which is isomorphic to the spin-embedding of Delta.},
author       = {De Bruyn, Bart},
issn         = {0218-0006},
journal      = {ANNALS OF COMBINATORICS},
keyword      = {dual polar space,isometric embedding,hyperplane,spin-embedding,SPIN-EMBEDDINGS,HYPERPLANES},
language     = {eng},
number       = {3},
pages        = {307--318},
title        = {A property of isometric mappings between dual polar spaces of type DQ(2n,K)},
url          = {http://dx.doi.org/10.1007/s00026-010-0061-6},
volume       = {14},
year         = {2010},
}

```
Chicago
De Bruyn, Bart. 2010. “A Property of Isometric Mappings Between Dual Polar Spaces of Type DQ(2n,K).” Annals of Combinatorics 14 (3): 307–318.
APA
De Bruyn, B. (2010). A property of isometric mappings between dual polar spaces of type DQ(2n,K). ANNALS OF COMBINATORICS, 14(3), 307–318.
Vancouver
1.
De Bruyn B. A property of isometric mappings between dual polar spaces of type DQ(2n,K). ANNALS OF COMBINATORICS. 2010;14(3):307–18.
MLA
De Bruyn, Bart. “A Property of Isometric Mappings Between Dual Polar Spaces of Type DQ(2n,K).” ANNALS OF COMBINATORICS 14.3 (2010): 307–318. Print.