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

Abstract

We obtain the symplectic group $\SP(V)$ as the universal completion of an amalgam of low rank subgroups akin to Levi components. We let $\SP(V)$ act flag-transitively on the geometry of maximal rank subspaces of $V$. We show that this geometry and its rank $\ge 3$ 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.