Direct Constructions of Hyperplanes of Dual Polar Spaces Arising from Embeddings

作者：De Bruyn Bart^*

来源：Annals of Combinatorics, 2010, 14(2): 193-209.

DOI：10.1007/s00026-010-0056-3

• dual polar space
• hyperplane
• Grassmann-embedding
• spin-embedding

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.

• 出版日期2010-6