{"title":"RADU GROUPS ACTING ON TREES ARE CCR","authors":"LANCELOT SEMAL","doi":"10.1017/s1446788723000381","DOIUrl":null,"url":null,"abstract":"<p>We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$2$</span></span></img></span></span>-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$(d_0,d_1)$</span></span></img></span></span>-semi-regular trees such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$d_0,d_1\\in \\Theta $</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305152040603-0270:S1446788723000381:S1446788723000381_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$\\Theta $</span></span></img></span></span> is an asymptotically dense set of positive integers.</p>","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1446788723000381","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
We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting $2$-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for $(d_0,d_1)$-semi-regular trees such that $d_0,d_1\in \Theta $, where $\Theta $ is an asymptotically dense set of positive integers.
期刊介绍：
The Journal of the Australian Mathematical Society is the oldest journal of the Society, and is well established in its coverage of all areas of pure mathematics and mathematical statistics. It seeks to publish original high-quality articles of moderate length that will attract wide interest. Papers are carefully reviewed, and those with good introductions explaining the meaning and value of the results are preferred.
Published Bi-monthly
Published for the Australian Mathematical Society
$2$-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for 
$(d_0,d_1)$-semi-regular trees such that 
$d_0,d_1\in \Theta $, where 
$\Theta $ is an asymptotically dense set of positive integers.
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