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

(2011) ARS COMBINATORIA. 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.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-2027042

- author
- Bart De Bruyn UGent
- 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
- 2011
- 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
- copyright statement
*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.