A quasi Curtis–Tits–Phan theorem for the symplectic group

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

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 ...

A pr 2 00 6 A Quasi Curtis - Tits - Phan theorem for the symplectic group

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.

A symplectic slice theorem

We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle [Mar84, Mar85] and Guillemin and Sternberg [GS84] for canonical symmetries that have an associated momentum map. In these papers the momentum map played a crucial role in the construction of the tubular model. The...

a note on the affine subgroup of the symplectic group

we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition