The cohomology ring of weight varieties and polygon spaces

We use a theorem of Tolman and Weitsman to find explicit formul\ae for the rational cohomology rings of the symplectic reduction of flag varieties in C^n, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate the cohomology ring of the moduli space of $n$ points in CP^k, which is isomorphic to the Grassmannian of k-planes in C^n, by realizing it as a degenerate coadjoint orbit.