Greenberg-Shalom's Commensurator Hypothesis and Applications
Group Theory
2025-11-10 v3 Differential Geometry
Geometric Topology
Abstract
We discuss many surprising implications of a positive answer to a question raised in some cases by Greenberg in the s and more generally by Shalom in the early 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.
Keywords
Cite
@article{arxiv.2308.07785,
title = {Greenberg-Shalom's Commensurator Hypothesis and Applications},
author = {Nic Brody and David Fisher and Mahan Mj and Wouter van Limbeek},
journal= {arXiv preprint arXiv:2308.07785},
year = {2025}
}
Comments
Final version. To appear Expositiones Math. Significant rearrangement to make the article more accessible