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


Author: Yue Zhou
Journal: Proc. Amer. Math. Soc. 149 (2021), 2319-2331
MSC (2020): Primary 05A30, 33D70, 05E05
DOI: https://doi.org/10.1090/proc/15399
Published electronically: March 18, 2021
MathSciNet review: 4246785
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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 Károlyi, 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.


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Additional Information

Yue Zhou
Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410075, People’s Republic of China
Email: zhouyue@csu.edu.cn

Keywords: Zeilberger–Bressoud $q$-Dyson theorem, Kadell’s orthogonality conjecture, symmetric function, constant term identity
Received by editor(s): August 26, 2020
Published electronically: March 18, 2021
Additional Notes: This work was supported by the National Natural Science Foundation of China (11871204).
Communicated by: Patricia Hersh
Article copyright: © Copyright 2021 American Mathematical Society