Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the symplectic sp(4) algebra and its q-deformed versions are investigated. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. Three important reduction chains are obtained in both the classical and deformed cases. In the primary reduction, the SU(2) sub-structure can be interpreted as either the spin, isospin or angular momentum group, when the other two reductions can be interpreted as pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The u(2) subalgebras of sp(4) can also be deformed and their representations are reducible in the action spaces of sp(4) and decompose into irreducible representations.