A note on the spinembedding of the dual polar space DQ⁻(2n+1,K)
 Author
 Bart De Bruyn (UGent)
 Organization
 Abstract
 In [6], Cooperstein and Shult showed that the dual polar space DQ()(2n+1, K), K = Fq, admits a full projective embedding into the projective space PG(2(n)  1,K'), K' = Fq2. 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 abovementioned embedding of DQ() (2n + 1, K) into PG(2(n)  1, K') is polarized.
 Keywords
 absolutely universal embedding, polarized embedding, spinembedding, dual polar space, halfspin geometry, generating rank, GEOMETRIES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU2027042
 MLA
 De Bruyn, Bart. “A Note on the SpinEmbedding of the Dual Polar Space DQ^{−}(2n+1,K).” ARS COMBINATORIA, vol. 99, 2011, pp. 365–75.
 APA
 De Bruyn, B. (2011). A note on the spinembedding of the dual polar space DQ^{−}(2n+1,K). ARS COMBINATORIA, 99, 365–375.
 Chicago authordate
 De Bruyn, Bart. 2011. “A Note on the SpinEmbedding of the Dual Polar Space DQ^{−}(2n+1,K).” ARS COMBINATORIA 99: 365–75.
 Chicago authordate (all authors)
 De Bruyn, Bart. 2011. “A Note on the SpinEmbedding of the Dual Polar Space DQ^{−}(2n+1,K).” ARS COMBINATORIA 99: 365–375.
 Vancouver
 1.De Bruyn B. A note on the spinembedding of the dual polar space DQ^{−}(2n+1,K). ARS COMBINATORIA. 2011;99:365–75.
 IEEE
 [1]B. De Bruyn, “A note on the spinembedding of the dual polar space DQ^{−}(2n+1,K),” ARS COMBINATORIA, vol. 99, pp. 365–375, 2011.
@article{2027042, abstract = {{In [6], Cooperstein and Shult showed that the dual polar space DQ()(2n+1, K), K = Fq, admits a full projective embedding into the projective space PG(2(n)  1,K'), K' = Fq2. 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 abovementioned embedding of DQ() (2n + 1, K) into PG(2(n)  1, K') is polarized.}}, author = {{De Bruyn, Bart}}, issn = {{03817032}}, journal = {{ARS COMBINATORIA}}, keywords = {{absolutely universal embedding,polarized embedding,spinembedding,dual polar space,halfspin geometry,generating rank,GEOMETRIES}}, language = {{eng}}, pages = {{365375}}, title = {{A note on the spinembedding of the dual polar space DQ⁻(2n+1,K)}}, volume = {{99}}, year = {{2011}}, }