Commuting differential and difference operators associated to complex curves, II

We construct a commuting family of difference-evaluation operators, deforming the commuting family introduced in our earlier paper (math/9807145). We interpret them as the action of the center of quantum algebras in the space of intertwiners for a ``regular'' subalgebra. These algebras are the quantum groups associated with sl_2 and algebraic curves, introduced by V. Rubtsov and the first author (q-alg/9608005). In the case of rational curves, our operators coincide those provided by the Yangian action on the hypergeometric spaces of Tarasov and Varchenko (q-alg/9604011).