Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Huang, Zihao, Jiang, Wenlong, Zhou, Yue
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1014462950
OpenAlex ID: W7212041760