Separation of variables for the A₂ Ruijsenaars model and a new integral representation for the A₂ Macdonald polynomials.

Using the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric three-particle Ruijsenaars model (a relativistic generalization of the Calogero-Moser-Sutherland model). In the quantum case, an integral operator M is constructed from the Askey-Wilson contour integral. The operator M transforms the eigenfunctions of the commuting Hamiltonians (the Macdonald polynomials for the root sytem A2) into the factorized form S(y₁)S(y₂) where S(y) is a Laurent polynomial of one variable expressed in terms of the ₃φ₂(y) basic hypergeometric series. The inversion of M produces a new integral representation for the A₂ Macdonald polynomials. We also present some results and conjectures for the general n-particle case.