On the q-Dyson orthogonality problem

2019/11/28 by Yue Zhou, Zhou, Yue
Mathematics · #05A30 #05E05 #33D70 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1911.12479

openalex publication_date 2019/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Plethystic identities and mixed Hodge structures of character varieties

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