{"title":"由自由模块产生的不可还原的 \\(Y(\\mathfrak {gl}_2)\\)-模块","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":"{\"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}","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}
Irreducible \(Y(\mathfrak {gl}_2)\)-modules arising from free modules
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.
期刊介绍:
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.