A Quasi Curtis-Tits-Phan theorem for the symplectic group
Group Theory
2007-05-23 v1 Combinatorics
Abstract
We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups. The geometry consists of all subspaces of maximal rank in a vector space of maximal rank with respect to a symplectic form. The main result holds for fields of size at least 3. We analyze the geometry over the field of size 2 and describe its simply connected cover if different from the geometry.
Cite
@article{arxiv.math/0604300,
title = {A Quasi Curtis-Tits-Phan theorem for the symplectic group},
author = {Rieuwert J. Blok and Corneliu Hoffman},
journal= {arXiv preprint arXiv:math/0604300},
year = {2007}
}
Comments
34 pages