{"title":"P(n)的非齐次振子表示","authors":"Ling Chen","doi":"10.1007/s10114-025-3419-8","DOIUrl":null,"url":null,"abstract":"<div><p>We study inhomogeneous oscillator representations of the strange Lie superalgebras <i>P</i>(<i>n</i>) on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions. We obtain the composition series for these representations. The obtained irreducible modules are infinite dimensional. Some of them are not of highest-weight type and even not weight modules.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1717 - 1752"},"PeriodicalIF":0.9000,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inhomogeneous Oscillator Representations of P(n)\",\"authors\":\"Ling Chen\",\"doi\":\"10.1007/s10114-025-3419-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study inhomogeneous oscillator representations of the strange Lie superalgebras <i>P</i>(<i>n</i>) on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions. We obtain the composition series for these representations. The obtained irreducible modules are infinite dimensional. Some of them are not of highest-weight type and even not weight modules.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":\"41 7\",\"pages\":\"1717 - 1752\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10114-025-3419-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-025-3419-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n) on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions. We obtain the composition series for these representations. The obtained irreducible modules are infinite dimensional. Some of them are not of highest-weight type and even not weight modules.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.