Commensurators of normal subgroups of lattices
[Commensurateurs de sous-groupes normaux de réseaux]
Fisher, David1 ; Mj, Mahan2 ; van Limbeek, Wouter3
1Department of Mathematics, Rice University, 6100 Main St MS 136, Houston, TX 77005, USA
2School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Navy Nagar, Colaba, Mumbai, Maharashtra 400005, India
3Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045, USA
Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1099-1122

We study a question of Greenberg-Shalom concerning arithmeticity of discrete subgroups of semisimple Lie groups with dense commensurators. We answer this question positively for normal subgroups of lattices. This generalizes a result of the second author and T. Koberda for certain normal subgroups of arithmetic lattices in SO(n,1) and SU(n,1).

Nous étudions une question de Greenberg-Shalom concernant l’arithméticité des sous-groupes discrets des groupes de Lie semi-simples avec des commensurateurs denses. Nous répondons positivement à cette question pour les sous-groupes normaux des réseaux. Ceci généralise un résultat du second auteur et de T. Koberda pour certains sous-groupes normaux de réseaux arithmétiques dans SO(n,1) et SU(n,1).

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.274
Classification : 22E40, 20A05, 20G15
Keywords: Discrete subgroups of Lie groups, commensurated subgroups, locally compact groups
Mots-clés : Sous-groupes discrets de groupes de Lie, sous-groupes commensurables, groupes localement compacts

Fisher, David  1   ; Mj, Mahan  2   ; van Limbeek, Wouter  3

1 Department of Mathematics, Rice University, 6100 Main St MS 136, Houston, TX 77005, USA
2 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Navy Nagar, Colaba, Mumbai, Maharashtra 400005, India
3 Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Commensurators of normal subgroups of lattices},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {1099--1122},
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Fisher, David; Mj, Mahan; van Limbeek, Wouter. Commensurators of normal subgroups of lattices. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1099-1122. doi: 10.5802/jep.274

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