{"title":"Symmetric pairs and branching laws","authors":"Paul-Émile Paradan","doi":"10.1016/j.indag.2024.03.009","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span><span> be a compact connected Lie group and let </span><span><math><mi>H</mi></math></span> be a subgroup fixed by an involution. A classical result assures that the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>ℂ</mi></mrow></msub></math></span>-action on the flag variety <span><math><mi>F</mi></math></span> of <span><math><mi>G</mi></math></span> admits a finite number of orbits. In this article we propose a formula for the branching coefficients of the symmetric pair <span><math><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></math></span> that is parametrized by <span><math><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>ℂ</mi></mrow></msub><mo>∖</mo><mi>F</mi></mrow></math></span>.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 675-702"},"PeriodicalIF":0.8000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae-New Series","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357724000168","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let be a compact connected Lie group and let be a subgroup fixed by an involution. A classical result assures that the -action on the flag variety of admits a finite number of orbits. In this article we propose a formula for the branching coefficients of the symmetric pair that is parametrized by .
期刊介绍：
Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.
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