{"title":"Root involutions, real forms and diagrams","authors":"S. Marini , C. Medori , M. Nacinovich","doi":"10.1016/j.exmath.2024.125593","DOIUrl":null,"url":null,"abstract":"<div><p>We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing <span><math><mrow><mi>S</mi><mspace></mspace></mrow></math></span>- and <span><math><mi>Σ</mi></math></span>-<em>diagrams</em>, generalizing those of Satake and Vogan.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 5","pages":"Article 125593"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000604/pdfft?md5=445995afea316cbdb564083c3930d697&pid=1-s2.0-S0723086924000604-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086924000604","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing - and -diagrams, generalizing those of Satake and Vogan.
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