Generalized t-j Model

By parameterizing the t-j model we present a new electron correlation model with one free parameter for high-temperature superconductivity. This model is of $SU_{q}(1,2)$ symmetry. The energy spectrums are shown to be modulated by the free parameter in the model. The solution and symmetric structures of the Hilbert space, as well as the Bethe ansatz approach are discussed for special cases.