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Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd

(2009) MICHIGAN MATHEMATICAL JOURNAL. 58(1). p.195-212
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Abstract
It was proved earlier that there are 6 isomorphism classes of hyperplanes in the dual polar space (5,q)$, $ even, which arise from its Grassmann-embedding. In the present paper, we extend these results to the case that $ is odd. Specifically, we determine the orbits of the full automorphism group of (5,q)$, $ odd, on the projective points (or equivalently, the hyperplanes) of the projective space (13,q)$ which affords the universal embedding of (5,q)$.
Keywords
Grassmann-embedding, (symplectic) dual polar space, GEOMETRIES, ARISE, hyperplane

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Citation

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Chicago
Cooperstein, Bruce, and Bart De Bruyn. 2009. “Points and Hyperplanes of the Universal Embedding Space of the Dual Polar Space DW(5,q), q Odd.” Michigan Mathematical Journal 58 (1): 195–212.
APA
Cooperstein, B., & De Bruyn, B. (2009). Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd. MICHIGAN MATHEMATICAL JOURNAL, 58(1), 195–212.
Vancouver
1.
Cooperstein B, De Bruyn B. Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd. MICHIGAN MATHEMATICAL JOURNAL. 2009;58(1):195–212.
MLA
Cooperstein, Bruce, and Bart De Bruyn. “Points and Hyperplanes of the Universal Embedding Space of the Dual Polar Space DW(5,q), q Odd.” MICHIGAN MATHEMATICAL JOURNAL 58.1 (2009): 195–212. Print.
@article{879249,
  abstract     = {It was proved earlier that there are 6 isomorphism classes of hyperplanes in the dual polar space (5,q)\$, \$ even, which arise from its Grassmann-embedding. In the present paper, we extend these results to the case that \$ is odd. Specifically, we determine the orbits of the full automorphism group of (5,q)\$, \$ odd, on the projective points (or equivalently, the hyperplanes) of the projective space (13,q)\$ which affords the universal embedding of (5,q)\$.},
  author       = {Cooperstein, Bruce and De Bruyn, Bart},
  issn         = {0026-2285},
  journal      = {MICHIGAN MATHEMATICAL JOURNAL},
  keyword      = {Grassmann-embedding,(symplectic) dual polar space,GEOMETRIES,ARISE,hyperplane},
  language     = {eng},
  number       = {1},
  pages        = {195--212},
  title        = {Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd},
  url          = {http://dx.doi.org/10.1307/mmj/1242071688},
  volume       = {58},
  year         = {2009},
}

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