Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation

In this paper we fill some gaps in the arguments of our previous papers [1,2]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining relations of the Yang-Baxter algebra. Among other results we present a derivation of the functional relations satisfied by T and Q operators and a proof of the basic analyticity assumptions for these operators used in [1,2].