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 >= 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. (C) 2007 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 4662-4691 |
Number of pages | 30 |
Journal | Journal of Algebra |
Volume | 319 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Jun 2008 |
Keywords
- amalgam
- Tits' lemma
- opposite
- simply connected
- symplectic group