Nonstandard Lagrangian Submanifolds in CP^n

We use Hamiltonian actions to construct nonstandard (as opposed to $\RP^n$ and $T^n$) Lagrangian submanifolds of $\CP^n$. First of all, a quotient of $\RP^3$ by the dihedral group $D_3$ is a Lagrangian submanifold of $\CP^3$. Secondly, $\Su(n)/\Z_n$ are Lagrangian submanifolds of $\CP^{n^2-1}$.