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

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- Proc. Amer. Math. Soc.
**149**(2021), 2319-2331 Request permission

## 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.## References

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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
- 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
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 2319-2331 - MSC (2020): Primary 05A30, 33D70, 05E05
- DOI: https://doi.org/10.1090/proc/15399
- MathSciNet review: 4246785