A new family of extended generalized quadrangles

• Main Authors: Fra, Alberto Del., Pasechnik, Dmitrii V., Pasini, Antonio.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Online Access: https://hdl.handle.net/10356/95391; http://hdl.handle.net/10220/9281
• Institution: Nanyang Technological University

For every hyperovalOofPG(2,q) (qeven), we construct an extended generalized quadrangle with point-residues isomorphic to the generalized quadrangleT*2(O) of order(q-1, q+1).These extended generalized quadrangles are flag-transitive only whenq=2 or 4. Whenq=2 we obtain a thin-lined polar space with four planes on every line. Whenq=4 we obtain one of the geometries discovered by Yoshiara [28]. That geometry is produced in [28] as a quotient of another one, which is simply connected, constructed in [28] by amalgamation of parabolics. In this paper we also give a ‘topological’ construction of that simply connected geometry.