A deformed Sp(4,R) algebra and possible applications

Based on the idea of a dynamical symmetry group, algebraic models of nuclear structure have proven to be quite successful in describing a variety of collective nuclear spectra [1]. A common element in these models is the su(3) ⊃ so(3) reduction that defines a relation between the quadrupole degree of freedom of the system and its angular momentum, which is used to classify levels of the system [2]. Anticipating further nuclear structure analysis based on quantum-deformed (q-deformed) algebras, a q-analog of a two-dimensional model with q -deformed SU(3) as its dynamical symmetry group [3] is developed. An explicit realization in terms of q-tensor operators with respect to the standard suq(2) algebra is given. This group-subgroup structure yields a physical interpretation of the generators of the groups under consideration.