Every stationary character on an irreducible lattice of a higher-rank semisimple Lie group is a genuine character, yielding new rigidity and URS finiteness results.
Character rigidity for lattices and commensurators
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abstract
We prove an operator algebraic superrigidity statement for homomorphisms of irreducible lattices, and also their commensurators, in certain higher-rank groups into unitary groups of finite factors. This extends the authors' previous work regarding non-free measure-preserving actions, and also answers a question of Connes for such groups.
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Stationary characters on lattices of semisimple Lie groups
Every stationary character on an irreducible lattice of a higher-rank semisimple Lie group is a genuine character, yielding new rigidity and URS finiteness results.