𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains

IF 1.2 1区数学 Q1 MATHEMATICS Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-04-29 DOI:10.1515/crelle-2023-0015

H. Upmeier

引用次数: 0

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.

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𝐾-invariant有界对称域上的Hilbert模与奇异向量束

摘要本文证明了秩为𝑟的有界对称域上某些Hilbert模的“本征束”(定位束)是一个“奇异”向量束(线性纤维复解析空间)，它沿着长度为r+1 r+1的规范分层分解为齐次向量束的分层和。纤维是根据地层法向空间的表示理论来实现的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

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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