  Representations of coherent state Lie algebras on coherent state manifolds as
first order differential operators are presented. The explicit expressions of
the differential action of the generators of semisimple Lie groups determine
for linear Hamiltonians in the generators of the groups first order
differential equations of motion with holomorphic polynomials coefficients. For
hermitian symmetric manifolds the equations of motion are matrix Riccati
equations. It is presented the simplest example of the non-symmetric space
$SU(3)/S(U(1)\times U(1)\times U(1))$ where the polynomials describing the
equations of motion have the maximum degree 3.
