On diagonal actions of branch groups and the corresponding characters |
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Authors: | Artem Dudko Rostislav Grigorchuk |
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Affiliation: | 1. IMPAN, Warsaw, Poland;2. Texas A&M University, College Station, TX, USA |
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Abstract: | We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acting on a regular rooted tree acts absolutely non-freely on the boundary of the tree. Using this result and the symmetrized diagonal actions we construct for every countable branch group infinitely many different ergodic perfectly non-free actions, infinitely many II1-factor representations, and infinitely many continuous ergodic invariant random subgroups. |
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Keywords: | 20C15 20E08 37A05 Non-free action Character Factor representation Branch group |
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