COMMON STRUCTURES BETWEEN FINITE SYSTEMS AND CONFORMAL FIELD-THEORIES THROUGH QUANTUM GROUPS

We discuss in this paper algebraic structures that are common to finite integrable lattice systems and conformal field theories. The concept of quantum group plays a major role in our study, and a detailed theory of representations of Uq[SU(n+1)] for q a root of unity is given. We obtain in particular a discrete analog of the Feigin-Fuchs construction, with corresponding concepts of null vectors or unitarity. The modular transformation S-matrix is also obtained from finite lattice considerations. © 1990.