Bispectrality for the quantum Ruijs']jsenaars model and its integrable deformation

An elementary construction of the eigenfunctions for the quantum rational Ruijsenaars model with integer coupling parameter is presented. As a by-product, we establish the bispectral duality between this model and the trigonometric Calogero-Moser model. In particular, this gives a new way for calculating Jack polynomials. We propose also a certain one-parameter deformation of the Ruijsenaars model, proving its integrability and bispectrality. The generalizations related to other root systems and difference operators by Macdonald are considered. (C) 2000 American Institute of Physics. [S0022-2488(00)03908-6].