Generalized Cherednik-Macdonald identities

TL;DR

This paper generalizes Cherednik-Macdonald identities to include symmetrically dependent quasi-periods, bridging q-identities with Jackson p-integral identities and extending their applicability to modulus one parameters.

Contribution

It introduces a new class of identities that unify and extend existing Cherednik-Macdonald and Jackson p-integral identities involving root systems.

Findings

Derived generalized identities depending on two quasi-periods

Unified q-identities with Jackson p-integral identities

Extended identities to modulus one deformation parameters

Abstract

We derive generalizations of the Cherednik-Macdonald constant term identities associated to root systems which depend, besides on the usual multiplicity function, symmetrically on two quasi-periods. They are natural analogues of the Cherednik-Macdonald constant term q-identities in which the deformation parameter q is allowed to have modulus one. They unite the Cherednik-Macdonald constant term q-identities with closely related Jackson p-integral identities due to Macdonald, where the deformation parameter p is related to q by modular inversion.