Geometric and Functional Analysis

, Volume 23, Issue 5, pp 1631–1683 | Cite as

Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity

  • Yehuda ShalomEmail author
  • George A. Willis


The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.


Normal Subgroup Algebraic Group Central Extension Chevalley Group Open Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of MathematicsTel-Aviv UniversityTel-AvivIsrael
  3. 3.School of Mathematical and Physical SciencesUniversity ofNewcastleCallaghanAustralia

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