1 research outputs found
Quadrangles embedded in metasymplectic spaces
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