NEW R-MATRICES ASSOCIATED WITH FINITE DIMENSIONAL REPRESENTATIONS OF UQ(SL(2)) AT ROOTS OF UNITY

We construct the R-matrix which intertwines between "semi-cyclic" representations of U(q)(sl(2)) with q3 = 1. When q(p) = 1 (for odd p), we call semi-cyclic representations those of dimension p which are characterized by the following value of the center of U(q)(sl(2)): E(p) = 0, F(p) = chi, KAPPA(p) = lambda-p. As in the cyclic case, the values of x and lambda-p of two different representations for which the intertwiner exists are constrained to lie on an algebraic curve, chi = kappa(1 -lambda-p). The main interest of our approach is that we do not need to resort to the affine extension of U(q)(sl(2)) in order to construct a spectral-dependent R-matrix.