On geometric SDPS-sets of elliptic dual polar spaces

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

De Bruyn, Bart

关键词: Dual polar space;    Half-spin geometry;    SDPS-set Spin embedding;    Hyperplane;    Valuation;   

DOI  :  10.1016/j.jcta.2009.07.009

来源: Elsevier

【 摘 要 】

Let n E N \ (0. 11 and let K and K' be fields such that K' is a quadratic Galois extension of K. Let Q -(2n + 1. K) be a nonsingular quadric of Witt index n in PG(2n + 1. K) whose associated quadratic form defines a nonsingular quadric Q+(2n + 1,11C) of Witt index n 1 in PG(2n + 1,1K'). For even n, we define a class of SDPS-sets of the dual polar space DQ -(2n + 1,1K) associated to Q -(2n +1, Cd), and call its members geometric SDPS-sets. We show that geometric SDPS-sets of DQ -(2n + 1,1K) are unique up to isomorphism and that they all arise from the spin embedding of DQ -(2n + 1, K). We will use geometric SOPS-sets to describe the structure of the natural embedding of D Q -(2n +1, K) into one of the half-spin geometries for Q (2n -1- 1. K'). C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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