English

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