Elliptic Ruijsenaars operators and functional equations

We study mutually commutative difference operators introduced by Ruijsenaars, which are regarded as elliptic analogs of Macdonald operators and consist of the Jacobi theta functions and shift operators. These operators are constructed in terms of R -operators due to Shibukawa and Ueno or root algebras introduced by Cherednik, which give rise to a set of functional equations. We investigate solutions of these functional equations for generalizations of elliptic Ruijsenaars operators.