On Cherednik-macdonald–mehta Identities

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...

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...

Some Constant Term Identities of Cherednik-macdonald-mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A (1) 1 . We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher-level generalizations of Cherednik’s Macdonald and Macdonald-Mehta co...

Diierence Macdonald-mehta Conjecture

DOUBLE HECKE ALGEBRAS 3 Nonsymmetric polynomials

0. Introduction 1. Affine Weyl groups (Reduction modulo W ) 2. Double Hecke algebras (Automorphisms, Demazure-Lusztig operators) 3. Macdonald polynomials (Intertwining operators) 4. Fourier transform on polynomials (Four transforms) 5. Jackson integrals (Macdonald’s η-identities) 6. Semisimple and pseudo-unitary representations (Main Theorem) 7. Spherical representations (Semisimple spherical r...