Eigenvalues and eigenstates of the s ell_q(2)-invariant Universal R-operator defined for cyclic representations at roots of unity

The s ell_q(2) representations are realized in the space of polynomials for general and exceptional values of deformation parameter q and on finite set of theta-functions for cyclic representation corresponding to q^N = +/- 1, which are a natural extension of the polynomials. The complete set of eigenstates of the Universal R-matrix are constructed and corresponding eigenvalues are calculated.