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

2022/10/24 by Guoce Xin, Yue Zhou, Xin, Guoce +1 · 1 citation
Mathematics · #05A30 #05E05 #33D70 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2210.13469

openalex publication_date 2022/10/24 · openalex created_date 2022/11/01 · openalex updated_date 2026/07/28

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. This conjecture was proved and extended by Károlyi, Nagy, Petrov and Volkov in 2015. In this paper, we obtain two symmetric function generalizations of the q-Baker--Forrester ex-conjecture. These includes: (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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• Koba-Nielsen local zeta functions, convex subsets, and generalized Selberg-Mehta-Macdonald and Dotsenko-Fateev-like integrals

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