Valuations and hyperplanes of dual polar spaces

Bart De Bruyn, Pieter Vandecasteele
2005 Journal of combinatorial theory. Series A  
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
more » ... will also give rise to a geometric hyperplane of the dual polar space.
doi:10.1016/j.jcta.2005.02.001 fatcat:n3jaehrqdzbitid66rbeiplspm