The uniqueness of the SDPS-set of the symplectic dual polar space DW(4n-1, q), n>=2
نویسنده
چکیده
SDPS-sets are very nice sets of points in dual polar spaces which themselves carry the structure of dual polar spaces. They were introduced in [8] because they gave rise to new valuations and hyperplanes of dual polar spaces. In the present paper, we show that the symplectic dual polar space DW (4n− 1, q), n ≥ 2, has up to isomorphisms a unique SDPS-set.
منابع مشابه
The uniqueness of the SDPS - set of the symplectic dual polar space DW ( 4 n − 1 , q ) , n ≥ 2 Bart
SDPS-sets are very nice sets of points in dual polar spaces which themselves carry the structure of dual polar spaces. They were introduced in [8] because they gave rise to new valuations and hyperplanes of dual polar spaces. In the present paper, we show that the symplectic dual polar space DW (4n− 1, q), n ≥ 2, has up to isomorphisms a unique SDPS-set.
متن کامل3 DW ( 2 n , q ) , n ≥ 3 , has no ovoid : A single proof
An ovoid of a dual polar space ∆ is a point set meeting every line of ∆ in exactly one point. For the symplectic dual polar space DW (6, q), Cooperstein and Pasini [2] have recently proved no ovoid exists if q is odd. Earlier, Shult has proved the same for even q (cf. [3, 2.8]). In this paper, we prove the non-existence of ovoids in DW (6, q) independently from the parity of q. MSC 2000: 51A15,...
متن کاملGenerating Symplectic and Hermitian Dual Polar Spaces over Arbitrary Fields Nonisomorphic to F2
Cooperstein [6], [7] proved that every finite symplectic dual polar space DW (2n− 1, q), q 6= 2, can be generated by ( 2n n ) − ( 2n n−2 ) points and that every finite Hermitian dual polar space DH(2n − 1, q2), q 6= 2, can be generated by (2n n ) points. In the present paper, we show that these conclusions remain valid for symplectic and Hermitian dual polar spaces over infinite fields. A conse...
متن کاملOn isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces
Let n ≥ 2, let K,K′ be fields such that K′ is a quadratic Galoisextension of K and let θ 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′, θ). We prove that the projective embedding of DW (2n − 1,K) induced by the Grassmann-embedding of DH(2n − 1,K′, θ) is ...
متن کاملThe hyperplanes of DW(5,F) arising from the Grassmann embedding
The hyperplanes of the symplectic dual polar space DW (5,F) that arise from the Grassmann embedding have been classified in [B.N. Cooperstein and B. De Bruyn. Points and hyperplanes of the universal embedding space of the dual polar space DW (5, q), q odd. Michigan Math. J., 58:195–212, 2009.] in case F is a finite field of odd characteristic, and in [B. De Bruyn. Hyperplanes of DW (5,K) with K...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 30 شماره
صفحات -
تاریخ انتشار 2009