Fermion System with Quantum Group Symmetry and Usual Fermion Realizations of S1_q(2)

The usual fermion realizations of quantum algebra sl_q(2) defining higher-dimensional representations are built in this letter. Using them, we construct a usual fermion system with quantum group symmetry of sl_q(2) as a q-deformation of the pairing correlation model in many-body problems. Its energy spectra are exactly solved out from the representation theory of sl_q(2).