A symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem

TL;DR

This paper introduces a new symmetric function generalization of the $q$-Dyson theorem, providing a simplified product-form expression for the constant term, building on previous conjectures and proofs in the area.

Contribution

It presents a novel symmetric function generalization of the $q$-Dyson identity with a straightforward product formula, extending Kadell's conjecture.

Findings

Derived a new symmetric function generalization of the $q$-Dyson identity.

Obtained a simple product-form expression for the generalized constant term.

Extended previous conjectures with a slight variable change.

Abstract

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem or the $q$-Dyson constant term identity. This conjecture was proved by K\'{a}rolyi, Lascoux and Warnaar in 2015. In this paper, by slightly changing the variables of Kadell's conjecture, we obtain another symmetric function generalization of the $q$-Dyson constant term identity. This new generalized constant term admits a simple product-form expression.