Quantum mechanics of integrable spins on coadjoint orbits

We investigate classical integrable spins defined on the reduced phase spaces of the coadjoint orbits of G = SU(N) group and their quantum mechanics. After discussions on a complete set of commuting functions on each orbit and construction of integrable spin models on flag manifolds, we quantize a concrete example of integrable spins on the SU(3) flag manifold in the coherent state quantization scheme and solve explicitly the time-dependent Schrodinger equation.