Coupling between the group-related coherent states

When two representations of the Lie algebra are coupled, the coupling integ ral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coeffi cients. The explicit expressions of these kernels for SU(2), SO(4) and SUq( 2) are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-re lated coherent states corresponding to two different schemes ale introduced , and the relations between these kernels and the general recoupling coeffi cients are obtained. The properties of these kernels are discussed.