Valuations and hyperplanes of dual polar spaces
نویسندگان
چکیده
Valuations were introduced in De Bruyn andVandecasteele (Valuations of near polygons, preprint, 2004) as a very important tool for classifying near polygons. In the present paperwe study valuations of dual polar spaces.Wewill introduce the class of theSDPS-valuations and characterize these valuations. We will show that a valuation of a finite thick dual polar space is the extension of an SDPS-valuation if and only if no induced hex valuation is ovoidal or semi-classical. Each SDPS-valuation will also give rise to a geometric hyperplane of the dual polar space. © 2005 Elsevier Inc. All rights reserved. MSC: 51A50; 51E12; 51E20
منابع مشابه
The uniqueness of the SDPS-set of the symplectic dual polar space DW(4n-1, q), n>=2
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.
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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.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 112 شماره
صفحات -
تاریخ انتشار 2005