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Direct constructions of hyperplanes of dual polar spaces arising from embeddings

Bart De Bruyn (UGent)
(2010) ANNALS OF COMBINATORICS. 14(2). p.193-209
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Abstract
Let e be one of the following full projective embeddings of a finite dual polar space Delta of rank n >= 2: (i) The Grassmann-embedding of the symplectic dual polar space Delta congruent to DW(2n 1,q); (ii) the Grassmann-embedding of the Hermitian dual polar space Delta congruent to DH(2n-1, q(2)); (iii) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(2n, q); (iv) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(-)(2n+ 1, q). Let H-e denote the set of all hyperplanes of Delta arising from the embedding e. We give a method for constructing the hyperplanes of H-e without implementing the embedding e and discuss (possible) applications of the given construction.
Keywords
OVOIDS, FINITE-FIELDS, GENERATION, spin-embedding, Grassmann-embedding, dual polar space, hyperplane

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Citation

Please use this url to cite or link to this publication:

Chicago
De Bruyn, Bart. 2010. “Direct Constructions of Hyperplanes of Dual Polar Spaces Arising from Embeddings.” Annals of Combinatorics 14 (2): 193–209.
APA
De Bruyn, B. (2010). Direct constructions of hyperplanes of dual polar spaces arising from embeddings. ANNALS OF COMBINATORICS, 14(2), 193–209.
Vancouver
1.
De Bruyn B. Direct constructions of hyperplanes of dual polar spaces arising from embeddings. ANNALS OF COMBINATORICS. 2010;14(2):193–209.
MLA
De Bruyn, Bart. “Direct Constructions of Hyperplanes of Dual Polar Spaces Arising from Embeddings.” ANNALS OF COMBINATORICS 14.2 (2010): 193–209. Print.
@article{1105428,
  abstract     = {Let e be one of the following full projective embeddings of a finite dual polar space Delta of rank n {\textrangle}= 2: (i) The Grassmann-embedding of the symplectic dual polar space Delta congruent to DW(2n 1,q); (ii) the Grassmann-embedding of the Hermitian dual polar space Delta congruent to DH(2n-1, q(2)); (iii) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(2n, q); (iv) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(-)(2n+ 1, q). Let H-e denote the set of all hyperplanes of Delta arising from the embedding e. We give a method for constructing the hyperplanes of H-e without implementing the embedding e and discuss (possible) applications of the given construction.},
  author       = {De Bruyn, Bart},
  issn         = {0218-0006},
  journal      = {ANNALS OF COMBINATORICS},
  keyword      = {OVOIDS,FINITE-FIELDS,GENERATION,spin-embedding,Grassmann-embedding,dual polar space,hyperplane},
  language     = {eng},
  number       = {2},
  pages        = {193--209},
  title        = {Direct constructions of hyperplanes of dual polar spaces arising from embeddings},
  url          = {http://dx.doi.org/10.1007/s00026-010-0056-3},
  volume       = {14},
  year         = {2010},
}

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