Boson realization of sp(4, R). II. The generating kernel formulation

In a previous paper of this series, the matrix elements were discussed with respect to boson states of an operator K2 required for the boson realization of the sp(4, R) Lie algebra. In the present paper, it is shown that these matrix elements can be obtained from a generating kernel given by the overlap of sp(4, R) coherent states. The results have relevance for the determination of the matrix elements of the generators of the sp(4, R) Lie algebra with respect to the basis of irreps of the positive discrete series for the corresponding group, and are, in principle, generalizable to symplectic algebras of higher dimensions