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

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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.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA

    Yehuda Shalom

  2. Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel

    Yehuda Shalom

  3. School of Mathematical and Physical Sciences, University ofNewcastle, Building V, Callaghan, 2308, Australia

    George A. Willis

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  1. Yehuda Shalom
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  2. George A. Willis
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Correspondence to Yehuda Shalom.

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Shalom, Y., Willis, G.A. Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity. Geom. Funct. Anal. 23, 1631–1683 (2013). https://doi.org/10.1007/s00039-013-0236-5

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