A generalization of Kadell's orthogonality ex-conjecture
Combinatorics
2026-05-19 v2
Abstract
In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud -Dyson constant term identity. The non-zero part of Kadell's conjecture is a constant term identity indexed by a weak composition . This conjecture was first proved by K\'{a}rolyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above constant term when all parts of the composition are distinct. In 2021, Zhou obtained a recursion for this constant term for an arbitrary composition . In this paper, by categorizing the variables into two parts, we generalize Zhou's result.
Cite
@article{arxiv.2603.08041,
title = {A generalization of Kadell's orthogonality ex-conjecture},
author = {Zihao Huang and Wenlong Jiang and Yue Zhou},
journal= {arXiv preprint arXiv:2603.08041},
year = {2026}
}