### A note on the spin-embedding of the dual polar space DQ⁻(2n+1,K)

Bart De Bruyn UGent (2011) 99. p.365-375
abstract
In [6], Cooperstein and Shult showed that the dual polar space DQ(-)(2n+1, K), K = F-q, admits a full projective embedding into the projective space PG(2(n) - 1,K'), K' = F-q2. They also showed that this embedding is absolutely universal. The proof in [6] makes use of counting arguments and group representation theory. Because of the use of counting arguments, the proof cannot be extended automatically to the infinite case. In this note, we shall give a different proof of their results, thus showing that their conclusions remain valid for infinite fields as well. We shall also show that the above-mentioned embedding of DQ(-) (2n + 1, K) into PG(2(n) - 1, K') is polarized.
author
organization
alternative title
A note on the spin-embedding of the dual polar space DQ^-(2n+1,K)
A note on the spin-embedding of the dual polar space DQ(-)(2n+1,K)
year
type
journalArticle (original)
publication status
published
subject
keyword
absolutely universal embedding, polarized embedding, spin-embedding, dual polar space, half-spin geometry, generating rank, GEOMETRIES
journal title
ARS COMBINATORIA
Ars Comb.
volume
99
pages
365 - 375
Web of Science type
Article
Web of Science id
000288971800031
JCR category
MATHEMATICS
JCR impact factor
0.268 (2011)
JCR rank
261/288 (2011)
JCR quartile
4 (2011)
ISSN
0381-7032
language
English
UGent publication?
yes
classification
A1
I have transferred the copyright for this publication to the publisher
id
2027042
handle
http://hdl.handle.net/1854/LU-2027042
date created
2012-02-10 13:52:16
date last changed
2014-01-22 08:40:48
```@article{2027042,
abstract     = {In [6], Cooperstein and Shult showed that the dual polar space DQ(-)(2n+1, K), K = F-q, admits a full projective embedding into the projective space PG(2(n) - 1,K'), K' = F-q2. They also showed that this embedding is absolutely universal. The proof in [6] makes use of counting arguments and group representation theory. Because of the use of counting arguments, the proof cannot be extended automatically to the infinite case. In this note, we shall give a different proof of their results, thus showing that their conclusions remain valid for infinite fields as well. We shall also show that the above-mentioned embedding of DQ(-) (2n + 1, K) into PG(2(n) - 1, K') is polarized.},
author       = {De Bruyn, Bart},
issn         = {0381-7032},
journal      = {ARS COMBINATORIA},
keyword      = {absolutely universal embedding,polarized embedding,spin-embedding,dual polar space,half-spin geometry,generating rank,GEOMETRIES},
language     = {eng},
pages        = {365--375},
title        = {A note on the spin-embedding of the dual polar space DQ\unmatched{207b}(2n+1,K)},
volume       = {99},
year         = {2011},
}

```
Chicago
De Bruyn, Bart. 2011. “A Note on the Spin-embedding of the Dual Polar Space DQ(2n+1,K).” Ars Combinatoria 99: 365–375.
APA
De Bruyn, B. (2011). A note on the spin-embedding of the dual polar space DQ(2n+1,K). ARS COMBINATORIA, 99, 365–375.
Vancouver
1.
De Bruyn B. A note on the spin-embedding of the dual polar space DQ(2n+1,K). ARS COMBINATORIA. 2011;99:365–75.
MLA
De Bruyn, Bart. “A Note on the Spin-embedding of the Dual Polar Space DQ(2n+1,K).” ARS COMBINATORIA 99 (2011): 365–375. Print.