Multiplicity in restricting small representations

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2022-03-11 DOI:10.3792/pjaa.98.004

Toshiyuki Kobayashi

引用次数: 2

Abstract

: We give a geometric criterion for the bounded multiplicity property of ‘‘small’’ inﬁnite-dimensional representations of real reductive Lie groups in both induction and restrictions. In particular, for a reductive symmetric pair ð G; H Þ , we determine the reductive subgroups G 0 having the property that any irreducible H -distinguished admissible representations of G are of bounded multiplicity when restricted to G 0 .

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限制小表示的多重性

我们给出了实约李群的“小”无限维表示在归纳和限制条件下的有界多重性的一个几何判据。特别是，对于约化对称对ð G;H Þ，我们确定了可约子群g0，它具有G的任何不可约H可分辨的可容许表示在g0内具有有界复数的性质。

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

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.