Non-uniform higher-rank lattices are character rigid

Alon Dogon; Michael Glasner; Yuval Gorfine; Liam Hanany; Arie Levit

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arXiv · 2507.21862

Non-uniform higher-rank lattices are character rigid

Alon Dogon·Michael Glasner·Yuval Gorfine·Liam Hanany·Arie Levit

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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.

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Alon Dogon, Michael Glasner, Yuval Gorfine, Liam Hanany, Arie Levit. 2025-07-29. Non-uniform higher-rank lattices are character rigid. https://arxiv.org/abs/2507.21862

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