Vector-coherent-state theory as a theory of induced representations

A general definition is given of vector-coherent state (VCS) representation theory. It is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases. The associated K-matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting VCS representations from larger representations in which they are embedded and for determining the Hermitian form, with respect to which an isometric-equivalent representation is, in fact, isometric.