Integral operator solution of the Yang-Baxter equation based on the elliptic beta integral

A general solution of the Yang-Baxter equation is
constructed as an integral operator with an elliptic hypergeometric
kernel acting in the space of functions of two complex variables.
It intertwines the product of two standard L-operators associated with
the Sklyanin algebra (an elliptic deformation of sl(2)). This R-matrix
is constructed from three operators generating the permutation
group of four parameters entering L-operators. Validity
of the Coxeter relations (including the star-triangle relation) is
based on the elliptic beta integral evaluation and corresponding
Bailey lemma. This is a joint work with S.D. Derkachov.