{"paper":{"title":"On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Artem Dudko, Rostislav Grigorchuk","submitted_at":"2015-08-22T01:49:41Z","abstract_excerpt":"We study Koopman and quasi-regular representations corresponding to the action of arbitrary weakly branch group G on the boundary of a rooted tree T. One of the main results is that in the case of a quasi-invariant Bernoulli measure on the boundary of T the corresponding Koopman representation of G is irreducible (under some general conditions). We also show that quasi-regular representations of G corresponding to different orbits and Koopman representations corresponding to different Bernoulli measures on the boundary of T are pairwise disjoint. This gives two continual collections of pairwis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05452","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}