Locally subquadrangular hyperplanes in symplectic and Hermitian dual polar spaces

In [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 if their lines contain more than three points.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Bart De Bruyn
• Keywords: Dual Polar Spaces, EJC 2007, EJC 2010, Hermitian Dual Polar, Subquadrangular Hyperplanes