English

A Quasi Curtis-Tits-Phan theorem for the symplectic group

Group Theory 2008-05-20 v1 Combinatorics

Abstract

We obtain the symplectic group \SP(V)\SP(V) as the universal completion of an amalgam of low rank subgroups akin to Levi components. We let \SP(V)\SP(V) act flag-transitively on the geometry of maximal rank subspaces of VV. We show that this geometry and its rank 3\ge 3 residues are simply connected with few exceptions. The main exceptional residue is described in some detail. The amalgamation result is then obtained by applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups.

Keywords

Cite

@article{arxiv.0805.2680,
  title  = {A Quasi Curtis-Tits-Phan theorem for the symplectic group},
  author = {Rieuwert J. Blok Corneliu Hoffman},
  journal= {arXiv preprint arXiv:0805.2680},
  year   = {2008}
}