The coherent state on SUq(2) homogeneous space

The generalized coherent states for quantum groups introduced by Jurco and StovIcek are studied for the simplest example SUq(2) in full detail. It is shown that the normalized SUq(2) coherent states enjoy the property of completeness, and allow a resolution of the unity. This feature is expected to play a key role in the application of these coherent states in physical models. The homogeneous space of SUq(2), i.e. the q-sphere of Podles, is reproduced in complex coordinates by using the coherent states. Differential calculus in the complex form on the homogeneous space is developed. The high spin limit of the SUq(2) coherent states is also discussed.