Non-uniform higher-rank lattices are character rigid

TL;DR

This paper proves character rigidity for non-uniform higher-rank lattices in semisimple groups, confirming a long-standing conjecture and extending rigidity results to a broad class of groups and actions.

Contribution

It establishes character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic not 2, generalizing previous results.

Findings

Proves character rigidity for non-uniform higher-rank lattices

Confirms a conjecture of Stuck and Zimmer for these lattices

Implications for stabilizer rigidity and invariant random subgroups

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.