Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions (Q387888)

The first result of the paper under review concerns a question on orthogonality properties of multivariable Baker-Akhiezer (BA) functions. As an application, a simple derivation of the norm formula for Macdonald polynomials is derived. A second result presents a version of the Cherednik-Macdonald-Mehta integral identity for BA functions. This is a generalization of the self-duality of the Gaussian, a basic fact about the Fourier transforms. The paper finishes with an appendix written by the first author. Here, a version is proved of the summation formula that involves the Gaussian. The so-called twisted BA functions are also introduced. These serve as common eigenfunctions for quantum models of Macdonald-Ruijsenaars type, and seem to be new.