Valuations and hyperplanes of dual polar spaces |
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Authors: | Bart De Bruyn Pieter Vandecasteele |
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Affiliation: | Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000, Gent, Belgium |
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Abstract: | Valuations were introduced in De Bruyn and Vandecasteele (Valuations of near polygons,preprint, 2004) as a very important tool for classifying near polygons. In the present paper we study valuations of dual polar spaces. We will introduce the class of the SDPS-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. |
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Keywords: | Dual polar space Near polygon Hyperplane |
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