Twisted quantum affine superalgebra ?, ? invariant <B> R</B>-matrices and a new integrable electronic model

We describe the twisted affine superalgebra 0305-4470/30/12/018/img9 and its quantized version 0305-4470/30/12/018/img10. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point subsuperalgebra 0305-4470/30/12/018/img11. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two 0305-4470/30/12/018/img11 invariant R-matrices: one of them corresponds to 0305-4470/30/12/018/img10 and the other to 0305-4470/30/12/018/img14. Using the R-matrix for 0305-4470/30/12/018/img10, we construct a new 0305-4470/30/12/018/img11 invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger 0305-4470/30/12/018/img17 symmetry.