{"title":"E7(7) 的狄拉克级数","authors":"Yi-Hao Ding, Chao-Ping Dong, Lin Wei","doi":"10.1007/s11856-024-2658-1","DOIUrl":null,"url":null,"abstract":"<p>This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of <i>E</i><sub>7(7)</sub>. Enhancing the Helgason–Johnson bound in 1969 for the group <i>E</i><sub>7(7)</sub> is one key ingredient. Our calculation partially supports Vogan’s fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest <i>K</i>-types have multiplicities.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dirac series of E7(7)\",\"authors\":\"Yi-Hao Ding, Chao-Ping Dong, Lin Wei\",\"doi\":\"10.1007/s11856-024-2658-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of <i>E</i><sub>7(7)</sub>. Enhancing the Helgason–Johnson bound in 1969 for the group <i>E</i><sub>7(7)</sub> is one key ingredient. Our calculation partially supports Vogan’s fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest <i>K</i>-types have multiplicities.</p>\",\"PeriodicalId\":14661,\"journal\":{\"name\":\"Israel Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Israel Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-024-2658-1\",\"RegionNum\":2,\"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":"Israel Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-024-2658-1","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
This paper classifies all the Dirac series (that is, irreducible unitary representations having non-zero Dirac cohomology) of E7(7). Enhancing the Helgason–Johnson bound in 1969 for the group E7(7) is one key ingredient. Our calculation partially supports Vogan’s fundamental parallelepiped (FPP) conjecture. As applications, when passing to Dirac index, we continue to find cancellation between the even part and the odd part of Dirac cohomology. Moreover, for the first time, we find Dirac series whose spin lowest K-types have multiplicities.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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