Symplectic Dynamical Symmetries in Algebraic Models of Nuclear Structure

Based on a generalized reduction scheme for boson representations of symplectic algebras of the type Sp(4k, R), we consider the symplectic extension of a boson realization of compact unitary algebras for the k = 1, k = 3 and k = 6 cases, which have relevance in nuclear structure theory. First we review an application of the k = 1 case for the creation of a Sp(4, R) classification scheme, which is used for obtaining a generalized phenomenological description of important nuclear characteristics in terms of the classification quantum numbers for large sets of nuclei. Then for the k = 3 and k = 6 cases we outline some of the new possibilities that appear in the symplectic extensions of the Interacting Vector Boson Model (IVBM) and the Interacting Boson Model (IBM-2), respectively. The examples presented are used to describe the collective modes of the nuclear spectra in individual nuclei as well as in sequences of nuclei.