{"title":"最高权重模块和小单能表示的转移","authors":"Hai An He, Jing Song Huang, Kayue Daniel Wong","doi":"10.1007/s10114-024-3237-4","DOIUrl":null,"url":null,"abstract":"<div><p>We study the transfer between small special unipotent representations for all equal rank real forms of type <i>E</i><sub>6</sub> and <i>E</i><sub>7</sub>. As a consequence, one can verify these modules are unitarity using the results of Wallach and Zhu. Moreover, the <i>K</i>-spectra of these modules can be obtained explicitly.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Transfer of Highest Weight Modules and Small Unipotent Representations\",\"authors\":\"Hai An He, Jing Song Huang, Kayue Daniel Wong\",\"doi\":\"10.1007/s10114-024-3237-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the transfer between small special unipotent representations for all equal rank real forms of type <i>E</i><sub>6</sub> and <i>E</i><sub>7</sub>. As a consequence, one can verify these modules are unitarity using the results of Wallach and Zhu. Moreover, the <i>K</i>-spectra of these modules can be obtained explicitly.</p></div>\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-03-15\",\"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/s10114-024-3237-4\",\"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/s10114-024-3237-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Transfer of Highest Weight Modules and Small Unipotent Representations
We study the transfer between small special unipotent representations for all equal rank real forms of type E6 and E7. As a consequence, one can verify these modules are unitarity using the results of Wallach and Zhu. Moreover, the K-spectra of these modules can be obtained explicitly.
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.
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