{"title":"𝐾-invariant有界对称域上的Hilbert模与奇异向量束","authors":"H. Upmeier","doi":"10.1515/crelle-2023-0015","DOIUrl":null,"url":null,"abstract":"Abstract We show that the “eigenbundle” (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank 𝑟 is a “singular” vector bundle (linearly fibred complex analytic space) which decomposes as a stratified sum of homogeneous vector bundles along a canonical stratification of length r + 1 r+1 . The fibres are realized in terms of representation theory on the normal space of the strata.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains\",\"authors\":\"H. Upmeier\",\"doi\":\"10.1515/crelle-2023-0015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that the “eigenbundle” (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank 𝑟 is a “singular” vector bundle (linearly fibred complex analytic space) which decomposes as a stratified sum of homogeneous vector bundles along a canonical stratification of length r + 1 r+1 . The fibres are realized in terms of representation theory on the normal space of the strata.\",\"PeriodicalId\":54896,\"journal\":{\"name\":\"Journal fur die Reine und Angewandte Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal fur die Reine und Angewandte Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2023-0015\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal fur die Reine und Angewandte Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/crelle-2023-0015","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains
Abstract We show that the “eigenbundle” (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank 𝑟 is a “singular” vector bundle (linearly fibred complex analytic space) which decomposes as a stratified sum of homogeneous vector bundles along a canonical stratification of length r + 1 r+1 . The fibres are realized in terms of representation theory on the normal space of the strata.
期刊介绍：
The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.
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