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arXiv · 1911.12479

On the $q$-Dyson orthogonality problem

Yue Zhou
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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.

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Yue Zhou. 2019-11-28. On the $q$-Dyson orthogonality problem. https://arxiv.org/abs/1911.12479

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