{"title":"论量子群簇实现的多项式猜想","authors":"Ivan Chi-Ho Ip , Jeff York Ye","doi":"10.1016/j.jalgebra.2024.08.031","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.</div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the polynomiality conjecture of cluster realization of quantum groups\",\"authors\":\"Ivan Chi-Ho Ip , Jeff York Ye\",\"doi\":\"10.1016/j.jalgebra.2024.08.031\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.</div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002186932400499X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002186932400499X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the polynomiality conjecture of cluster realization of quantum groups
In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra to be universally polynomial. This resolves several conjectures by the first author on the polynomiality of the cluster realization of quantum group generators in different families of positive representations.
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