SEPARATION OF VARIABLES FOR THE A(2) RUIJSENAARS MODEL AND A NEW INTEGRAL-REPRESENTATION FOR THE A(2) MACDONALD POLYNOMIALS

Using the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric three-particle Ruijsenaar s model (a relativistic generalization of the Calogero-Moser-Sutherlan d model). In the quantum case, an integral operator M is constructed f rom the Askey-Wilson contour integral. The operator M transforms the e igenfunctions of the commuting Hamiltonians (the Macdonald polynomials for the root sytem A(2)) into the factorized form S(y(1))S(y(2)) wher e S(y) is a Laurent polynomial of one variable expressed in terms of t he (3) phi(2)(y) basic hypergeometric series. The inversion of M produ ces a new integral representation for the A(2) Macdonald polynomials. We also present some results and conjectures for the general n-particl e case.