The vertex-face correspondence and correlation functions of the fusion eight-vertex model

By making use of the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the k×k fusion eight-vertex model in terms of the corresponding fusion SOS model. Here k∈Z>0. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner-transfer matrices, the half-transfer matrices (vertex operators) and the tail operator. We give a realization of these lattice operators as well as the space of states as objects in the level k representation theory of the elliptic algebra Uq,p(slˆ2).