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arXiv · 2308.07785

Greenberg-Shalom's Commensurator Hypothesis and Applications

Nic Brody·David Fisher·Mahan Mj·Wouter van Limbeek
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Abstract

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.

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Nic Brody, David Fisher, Mahan Mj, Wouter van Limbeek. 2023-08-15. Greenberg-Shalom's Commensurator Hypothesis and Applications. https://arxiv.org/abs/2308.07785

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