Induced shift tensors in vector coherent state theory

It is shown that the so‐called shift tensors of Biedenharn and Louck have a natural expression within the framework of vector coherent state (VCS) theory. VCS theory was developed to give a systematic construction of the representations of Lie groups and to derive the corresponding matrices representing the elements of their Lie algebras. In this paper there are explicit realizations of shift tensors within the framework of VCS theory for semisimple Lie groups in terms of shift tensors for suitably defined subgroups.