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An AFLT-type generalization of the q-Baker--Forrester ex-conjecture
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 Károlyi, 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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BibTeX
@misc{huang2026aflttype,
title = {{An AFLT-type generalization of the $q$-Baker--Forrester ex-conjecture}},
author = {Zihao Huang and Wenlong Jiang and Yue Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05836},
eprint = {2609.05836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05836},
}
RIS
TY - UNPB
TI - An AFLT-type generalization of the q-Baker--Forrester ex-conjecture
AU - Zihao Huang
AU - Wenlong Jiang
AU - Yue Zhou
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05836
UR - https://arxiv.org/abs/2609.05836
AB - 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 Károlyi, 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.
ER -