Noncommutative Coordinates for Symplectic Representations

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