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On Some Extended Dual Polar Spaces, I

✍ Scribed by Satoshi Yoshiara


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
495 KB
Volume
15
Category
Article
ISSN
0195-6698

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πŸ“œ SIMILAR VOLUMES


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We address the classification problem of flag-transitive geometries with diagrams of the form 1

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Let n 2, let K, K be fields such that K is a quadratic Galoisextension of K and let ΞΈ denote the unique nontrivial element in Gal(K /K). Suppose the symplectic dual polar space DW (2n -1, K) is fully and isometrically embedded into the Hermitian dual polar space DH(2n -1, K , ΞΈ). We prove that the p

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It is demonstrated that the dual polar space of type Sp(2n, 2) can be generated as a geometry by 3 points when n = 4 and 5. In the latter case this affirmatively resolves a conjecture of Brouwer that the dimension of the universal projective embedding of this geometry is Ξ»(5).

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Let be a finite thick dual polar space, and let H be a hyperplane of . Calling the elements of of type 2 quads, we call a quad Ξ± βŠ‚ H singular (respectively subquadrangular or ovoidal) if H meets Ξ± in the perp of a point (respectively in a full subquadrangle or in an ovoid). A hyperplane is said to b

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It has been conjectured by A. E. Brouwer that the dimension of the universal embedding module of a dual polar space of type Sp 2n (2) is Following a point stabilizer approach of A. A. Ivanov and M. K. Bardoe, we investigate the dimensions of certain quotients of permutation modules for SL n (2) on