Quadrangles embedded in metasymplectic spaces
Combinatorics
2009-09-29 v1
Abstract
During the final steps in the classification of the Moufang quadrangles by Jacques Tits and Richard Weiss a new class of Moufang quadrangles unexpectedly turned up. Subsequently Bernhard Muhlherr and Hendrik Van Maldeghem showed that this class arises as the fixed points and hyperlines of certain involutions of a metasymplectic space (or equivalently a building of type F_4). In the same paper they also showed that other types of Moufang quadrangles can be embedded in a metasymplectic space as points and hyperlines. In this paper, we reverse the question: given a (thick) quadrangle embedded in a metasymplectic space as points and hyperlines, when is such a quadrangle a Moufang quadrangle?
Cite
@article{arxiv.0909.4960,
title = {Quadrangles embedded in metasymplectic spaces},
author = {Koen Struyve},
journal= {arXiv preprint arXiv:0909.4960},
year = {2009}
}