{"title":"Irreducible \\(Y(\\mathfrak {gl}_2)\\)-modules arising from free modules","authors":"Han Dai, Dashu Xu","doi":"10.1007/s00013-024-02068-9","DOIUrl":null,"url":null,"abstract":"<div><p>We classify a class of modules for the Yangian <span>\\(Y(\\mathfrak {gl}_2)\\)</span>, where the element <span>\\(e_{21}\\in Y(\\mathfrak {gl}_2)\\)</span> acts regularly. These modules can be realized by use of the differential operators. Moreover, we compute the central characters of these modules by employing the trick of formal generating series.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 6","pages":"605 - 613"},"PeriodicalIF":0.5000,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02068-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We classify a class of modules for the Yangian \(Y(\mathfrak {gl}_2)\), where the element \(e_{21}\in Y(\mathfrak {gl}_2)\) acts regularly. These modules can be realized by use of the differential operators. Moreover, we compute the central characters of these modules by employing the trick of formal generating series.
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Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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