{"title":"Weights for compact connected Lie groups","authors":"Radha Kessar, Gunter Malle, Jason Semeraro","doi":"10.1007/s00229-024-01538-2","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(\\ell \\)</span> be a prime. If <span>\\(\\textbf{G}\\)</span> is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from <span>\\(\\ell \\)</span>, and <span>\\(\\ell \\)</span> is a good prime for <span>\\(\\textbf{G}\\)</span>, we show that the number of weights of the <span>\\(\\ell \\)</span>-fusion system of <span>\\(\\textbf{G}\\)</span> is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of <span>\\(\\ell \\)</span>-stubborn subgroups in compact Lie groups.\n</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"57 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01538-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(\ell \) be a prime. If \(\textbf{G}\) is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from \(\ell \), and \(\ell \) is a good prime for \(\textbf{G}\), we show that the number of weights of the \(\ell \)-fusion system of \(\textbf{G}\) is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of \(\ell \)-stubborn subgroups in compact Lie groups.
期刊介绍:
manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.