Non-uniform higher-rank lattices are character rigid
Group Theory
2025-07-30 v1 Dynamical Systems
Operator Algebras
Representation Theory
Abstract
We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant random subgroups, confirming a conjecture of Stuck and Zimmer for non-uniform lattices in full generality.
Keywords
Cite
@article{arxiv.2507.21862,
title = {Non-uniform higher-rank lattices are character rigid},
author = {Alon Dogon and Michael Glasner and Yuval Gorfine and Liam Hanany and Arie Levit},
journal= {arXiv preprint arXiv:2507.21862},
year = {2025}
}
Comments
31 pages; includes an appendix