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

IF 1.2 2区数学 Q1 MATHEMATICS Transactions of the American Mathematical Society Pub Date : 2024-03-29 DOI:10.1090/tran/9142

Guoce Xin, Yue Zhou

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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 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 q -Baker–Forrester ex-conjecture. These include: (i) a q 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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△-贝克-福雷斯特前猜想的对称函数广义和塞尔伯格型积分

众所周知，著名的塞尔伯格积分等价于莫里斯常数项同一性。1998 年，贝克和福雷斯特猜想出了 q q - 莫里斯常数项同一性的一般化[J. Combin.Károlyi, Nagy, Petrov, and Volkov (KNPV) 在 2015 年证明并扩展了这一猜想[Adv. Math. 277 (2015), pp.］在本文中，我们得到了 q q -Baker-Forrester 前猜想的两个对称函数广义。它们包括(i) 完全对称函数与麦克唐纳多项式乘积的 q q -Baker-Forrester 型常数项同一性；(ii) KNPV 结果的完全对称函数广义化。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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