Generalized q-deformed symplectic sp(4) algebra for multi-shell applications

A multi-shell generalization of a fermion representation of the q-deformed compact symplectic spq(4) algebra is introduced. An analytic form for the action of two or more generators of the Spq (4) symmetry on the basis states is determined and the result used to derive formulae for the overlap between number-preserving states as well as for matrix elements of a model Hamiltonian. A second-order operator in the generators of Sp q(4) is identified that is diagonal in the basis set and that reduces to the Casimir invariant of the sp(4) algebra in the non-deformed limit of the theory. The results can be used in nuclear structure applications to calculate β-decay transition probabilities and to provide for a description of pairing and higher-order interactions in systems with nucleons occupying more than a single-j orbital