New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions

We present a general formula for constructing R-matrices with non-additive spectral parameters associated with a type-I quantum superalgebra. The spectral parameters originate from two one-parameter families of inequivalent finite-dimensional irreducible representations of the quantum superalgebra upon which the R-matrix acts. Applying to the quantum superalgebra $U_q(gl(2|1))$, we obtain the explicit expression for the $U_q(gl(2|1))$-invariant R-matrix which is of non-difference form in spectral parameters. Using this R-matrix we derive a new two-parameter integrable model of strongly correlated electrons with pure imaginary pair hopping terms.