On the $q$-Dyson orthogonality problem

Abstract

By combining the Gessel--Xin method with plethystic substitutions, we obtain a recursion for a symmetric function generalization of the $q$-Dyson constant term identity also known as the Zeilberger--Bressoud $q$-Dyson theorem. This yields a constant term identity which generalizes the non-zero part of Kadell's orthogonality ex-conjecture and a result of Károlyi, Lascoux and Warnaar.

27 pages

References in corpus (1)

• The Ring of Malcev-Neumann Series and the Residue Theorem

Cited by in corpus (2)

• A recursion for a symmetric function generalization of the $q$-Dyson constant term identity
• A symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem