Quadrangles embedded in metasymplectic spaces

Details Quadrangles embedded in metasymplectic spaces Quadrangles embedded in metasymplectic spaces

2009-09-27

arxiv.org/abs/0909.4960v1

Mathematics

Combinatorics

Scientific paper

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?

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