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

Yehuda Shalom, George A. Willis

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1631-1683
Number of pages53
JournalGeometric and Functional Analysis
Volume23
Issue number5
DOIs
StatePublished - Oct 2013

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