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arXiv · 2609.05836

An AFLT-type generalization of the $q$-Baker--Forrester ex-conjecture

Zihao Huang·Wenlong Jiang·Yue Zhou
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Abstract

The Habsieger--Kadell $q$-Morris constant term identity, which is equivalent to the famous $q$-Selberg integral, has been generalized in numerous ways since the 1980s. Among these, there are two important generalizations: (i) the $q$-Baker--Forrester ex-conjecture, which was conjectured by Baker and Forrester in 1998 and proved by K\'{a}rolyi, Nagy, Petrov and Volkov in 2015; (ii) the AFLT-type $q$-Morris identity (equivalently, the AFLT-type $q$-Selberg integral), which was obtained by Albion, Rains and Warnaar in 2021, as a $q$-analog of the result of Alba, Fateev, Litvinov and Tarnopolskiy (AFLT). In this paper, by the Gessel--Xin method and the Macdonald polynomials with prescribed symmetry, we unify these two generalizations.

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Zihao Huang, Wenlong Jiang, Yue Zhou. 2026-09-05. An AFLT-type generalization of the $q$-Baker--Forrester ex-conjecture. https://arxiv.org/abs/2609.05836

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