{"paper":{"title":"Boundary representations of hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.DS","authors_text":"{\\L}ukasz Garncarek","submitted_at":"2014-04-03T13:28:21Z","abstract_excerpt":"Let $\\Gamma$ be a Gromov hyperbolic group, endowed with an arbitrary left-invariant hyperbolic metric, quasi-isometric to a word metric. The action of $\\Gamma$ on its boundary $\\partial\\Gamma$ endowed with the Patterson-Sullivan measure $\\mu$, after an appropriate normalization, gives rise to a faithful unitary representation of $\\Gamma$ on $L^2(\\partial\\Gamma,\\mu)$. We show that these representations are irreducible, and give criteria for their unitary equivalence in terms of the metrics on $\\Gamma$. Special cases include quasi-regular representations on the Poisson boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0903","kind":"arxiv","version":2},"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"}