  Based on the vertex-face correspondence, we give an algebraic analysis
formulation of correlation functions of the $k\times k$ fusion eight-vertex
model in terms of the corresponding fusion SOS model. Here $k\in Z_{>0}$. 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
$U_{q,p}(\hat{sl}_2)$.
