The Dyson Realization of the Quantum Group SU(1,1) q and Its Coherent state

The Dyson realization of the quantum group SU(1,1) q is constructed and the transformation matrix, which turns the Dyson realization into the Holstein–Primakoff realization, is given. The coherent state for the Dyson realization is discussed and is found to be the q -deformed Weyl–Heisenberg coherent state.