  A closed (in terms of classical data) expression for a transition amplitude
between two generalized coherent states associated with a semisimple Lee
algebra underlying the system is derived for large values of the representation
highest weight, which corresponds to the quasiclssical approximation.
Consideration is based upon a path-integral formalism adjusted to quantization
of symplectic coherent-state manifolds that appear as one-rank coadjoint
orbits.
