Noncommutative Coordinates for Symplectic Representations

Daniele Alessandrini, Stevens Institute of Technology, Hoboken, New Jersey, Olivier Guichard, Universite de Strasbourg et CNRS, France, Eugen Rogozinnikov, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, and Anna Wienhard, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

1. Introduction 2. Symplectic group, Lagrangians 3. Invariants of Lagrangian subspaces 4. Moduli spaces of framed and decorated local systems 5. Local systems on quivers and their framings 6. $\mathcal {X}$-coordinates for maximal representations 7. Topology of the space of maximal framed representations 8. Singularities of the space of framed maximal representations into $Sp(4,\mathbf {R})$ 9. General $\mathcal {X}$-coordinates 10. $\mathcal {X}$-coordinates for representations into isogenic groups 11. $\mathcal {A}$-coordinates for decorated local systems A. Normal form for pair of quadratic forms