{"title":"△-贝克-福雷斯特前猜想的对称函数广义和塞尔伯格型积分","authors":"Guoce Xin, Yue Zhou","doi":"10.1090/tran/9142","DOIUrl":null,"url":null,"abstract":"<p>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 <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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 <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Baker–Forrester ex-conjecture. These include: (i) a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symmetric function generalizations of the 𝑞-Baker–Forrester ex-conjecture and Selberg-type integrals\",\"authors\":\"Guoce Xin, Yue Zhou\",\"doi\":\"10.1090/tran/9142\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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 <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"q\\\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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 <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"q\\\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Baker–Forrester ex-conjecture. These include: (i) a <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"q\\\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-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.</p>\",\"PeriodicalId\":23209,\"journal\":{\"name\":\"Transactions of the American Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/tran/9142\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/tran/9142","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Symmetric function generalizations of the 𝑞-Baker–Forrester ex-conjecture and Selberg-type integrals
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 qq-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 qq-Baker–Forrester ex-conjecture. These include: (i) a qq-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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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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