We address the classification problem of flag-transitive geometries with diagrams of the form 1
On Some Extended Dual Polar Spaces, I
β 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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π SIMILAR VOLUMES
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
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).
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± β 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
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