Realization of the Universal $s\ell_q(2)$-Symmetric $R$-Operator in a Function Space for General and Exceptional Values of the Deformation Parameter

Based on the realization of representations of the algebra $s\ell_q(2)$ in the space of polynomials for general values of the deformation parameter $q$ and on a finite tuple of theta functions, which are a natural generalization of polynomials, we construct the eigenstates and find the related eigenvalues of the universal $R$-operator for cyclic representations corresponding to $q^N=\pm1$.