{"title":"通过超级阿德勒型算子的矩形 $$mathcal {W}$$ - 上代数上的可积分系统","authors":"Sylvain Carpentier, Gahng Sahn Lee, Uhi Rinn Suh","doi":"10.1007/s00220-024-05042-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra <span>\\(\\mathfrak {gl}(m|n)\\)</span>. We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical <span>\\(\\mathcal {W}\\)</span>-superalgebras associated with <span>\\(\\mathfrak {gl}(m|n)\\)</span> and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular <span>\\(\\mathcal {W}\\)</span>-superalgebras.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 7","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05042-2.pdf","citationCount":"0","resultStr":"{\"title\":\"Integrable Systems on Rectangular \\\\(\\\\mathcal {W}\\\\)-Superalgebras via Super Adler-Type Operators\",\"authors\":\"Sylvain Carpentier, Gahng Sahn Lee, Uhi Rinn Suh\",\"doi\":\"10.1007/s00220-024-05042-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra <span>\\\\(\\\\mathfrak {gl}(m|n)\\\\)</span>. We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical <span>\\\\(\\\\mathcal {W}\\\\)</span>-superalgebras associated with <span>\\\\(\\\\mathfrak {gl}(m|n)\\\\)</span> and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular <span>\\\\(\\\\mathcal {W}\\\\)</span>-superalgebras.</p></div>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":\"405 7\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00220-024-05042-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00220-024-05042-2\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05042-2","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Integrable Systems on Rectangular \(\mathcal {W}\)-Superalgebras via Super Adler-Type Operators
In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra \(\mathfrak {gl}(m|n)\). We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical \(\mathcal {W}\)-superalgebras associated with \(\mathfrak {gl}(m|n)\) and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular \(\mathcal {W}\)-superalgebras.
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