The AFLT $q$-Morris constant term identity

TL;DR

This paper extends the Gessel--Xin Laurent series method to derive a new AFLT $q$-Morris constant term identity involving Macdonald polynomials, broadening the scope of constant term identities related to Selberg integrals.

Contribution

It introduces a novel AFLT $q$-Morris constant term identity for Macdonald polynomials using an extended Laurent series approach.

Findings

Derived a new $q$-Morris constant term identity for Macdonald polynomials.

Extended the Gessel--Xin method to handle AFLT type identities.

Connected constant term identities with Selberg integrals and Laurent polynomial techniques.

Abstract

It is well-known that the Selberg integral is equivalent to the Morris constant term identity. More generally, Selberg type integrals can be turned into constant term identities for Laurent polynomials. In this paper, by extending the Gessel--Xin method of the Laurent series proof of constant term identities, we obtain an AFLT type $q$-Morris constant term identity. That is a $q$-Morris type constant term identity for a product of two Macdonald polynomials.