  We consider finite-dimensional reductions of an integral operator with the
elliptic hypergeometric kernel describing the most general known solution of
the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced
R-operators reproduce at their bottom the standard Baxter's R-matrix for the
8-vertex model and Sklyanin's L-operator. The general formula has a remarkably
compact form and yields new elliptic solutions of the Yang-Baxter equation
based on the finite-dimensional representations of the elliptic modular double.
The same result is also derived using the fusion formalism.
