Symmetric function generalizations of the 𝑞-Baker–Forrester ex-conjecture and Selberg-type integrals

Xin, Guoce; Zhou, Yue

doi:10.1090/tran/9142

Symmetric function generalizations of the $q$-Baker–Forrester ex-conjecture and Selberg-type integrals
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by Guoce Xin and Yue Zhou;

Trans. Amer. Math. Soc. 377 (2024), 4303-4363

DOI: https://doi.org/10.1090/tran/9142

Published electronically: April 9, 2024

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Abstract:

It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the $q$-Morris constant term identity[J. Combin. Theory Ser. A 81 (1998), pp. 69–87]. This conjecture was proved and extended by Károlyi, Nagy, Petrov, and Volkov (KNPV) in 2015 [Adv. Math. 277 (2015), pp. 252–282]. In this paper, we obtain two symmetric function generalizations of the $q$-Baker–Forrester ex-conjecture. These include: (i) a $q$-Baker–Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV’s result.

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