Locally subquadrangular hyperplanes in symplectic and Hermitian dual polar spaces

Authors:
Bart De Bruyn
Affiliations:
Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281 (S22), B-9000 Gent, Belgium
Venue:
European Journal of Combinatorics
Year:
2010

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Finite Fields and Their Applications

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Abstract

In Pasini and Shpectorov (2001) [11] all locally subquadrangular hyperplanes of finite symplectic and Hermitian dual polar spaces were determined with the aid of counting arguments and divisibility properties of integers. In the present note we extend this classification to the infinite case. We prove that symplectic dual polar spaces and certain Hermitian dual polar spaces cannot have locally subquadrangular hyperplanes if their rank is at least three and their lines contain more than three points.