2-dimensional cyclic representations of Uq(sl(2)), C-G coefficients and a free fermion 8-vertex model

The authors give explicitly the 2-dimensional cyclic representations of quantum algebra Uq(sl(2)) with central extension. The C-G rule and the C-G coefficients are calculated and the intertwiner for tensor representations in different orders is constructed with C-G coefficients. This intertwiner is shown to be the R-matrix for an eight vertex model that satisfies the free Fermion condition and therefore gives an integrable model