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We propose a conjectural formula for correlation functions of the Z-invariant(inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. Itstates that correlation functions are linear combinations of products of threetranscendental functions, with theta functions and derivatives as coefficients.The transcendental functions are essentially logarithmic derivatives of thepartition function per site. The coefficients are given in terms of a linearfunctional on the Sklyanin algebra, which interpolates the usual trace onfinite dimensional representations. We establish the existence of thefunctional and discuss the connection to the geometry of the classical limit.We also conjecture that the Ansatz satisfies the reduced qKZ equation. As anon-trivial example of the Ansatz, we present a new formula for thenext-nearest neighbor correlation functions.Comment: 35 pages, 2 figures, final versio

Traces on the Sklyanin algebra and correlation functions of the eight-vertex model