Some Constant Term Identities of Cherednik-macdonald-mehta Type

Orthogonality Relations and Cherednik Identities for Multivariable Baker–akhiezer Functions

We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summati...

On Cherednik–macdonald–mehta Identities

In this note we give a proof of Cherednik’s generalization of Macdonald–Mehta identities for the root system An−1, using representation theory of quantum groups. These identities give an explicit formula for the integral of a product of Macdonald polynomials with respect to a “difference analogue of the Gaussian measure”. They were suggested by Cherednik, who also gave a proof based on represen...

On Cherednik-macdonald–mehta Identities

Diierence Macdonald-mehta Conjecture

An Elementary Approach to the Macdonald Identities*

Elementary proofs are given for the infinite families of Macdonald identities. The reflections of the Weyl group provide sign-reversing involutions which show that all terms not related to the constant term cancel.