Greenberg-Shalom's Commensurator Hypothesis and Applications
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912691928432640 |
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| author | Brody, Nic Fisher, David Mj, Mahan van Limbeek, Wouter |
| author_facet | Brody, Nic Fisher, David Mj, Mahan van Limbeek, Wouter |
| contents | We discuss many surprising implications of a positive answer to a question raised in some cases by Greenberg in the $`70$s and more generally by Shalom in the early $2000$s. We refer to this positive answer as the Greenberg-Shalom hypothesis. This hypothesis then says that any infinite discrete subgroup of a semisimple Lie group with dense commensurator is a lattice in a product of some factors. For some applications it is natural to extend the hypothesis to cover semisimple algebraic groups over other fields as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07785 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Greenberg-Shalom's Commensurator Hypothesis and Applications Brody, Nic Fisher, David Mj, Mahan van Limbeek, Wouter Group Theory Differential Geometry Geometric Topology 22E40, 53C35 We discuss many surprising implications of a positive answer to a question raised in some cases by Greenberg in the $`70$s and more generally by Shalom in the early $2000$s. We refer to this positive answer as the Greenberg-Shalom hypothesis. This hypothesis then says that any infinite discrete subgroup of a semisimple Lie group with dense commensurator is a lattice in a product of some factors. For some applications it is natural to extend the hypothesis to cover semisimple algebraic groups over other fields as well. |
| title | Greenberg-Shalom's Commensurator Hypothesis and Applications |
| topic | Group Theory Differential Geometry Geometric Topology 22E40, 53C35 |
| url | https://arxiv.org/abs/2308.07785 |