Universal R-matrix and functional relations

It seems that the most productive, although not comprehensive, modern approach to the theory of quantum integrable systems is the approach based on the concept of quantum group invented by Drinfeld and Jimbo. In this approach all the objects describing the model and related to its integrability originate from the universal R-matrix and the functional relations, principal for the integration procedure, are consequences of the properties of the appropriate representations of the quantum group. I will discuss the properties of the representations which are used to construct the objects entering functional relations, transfer operators and Q-operators, and demonstrate how they work.