{"paper":{"title":"On invariant subalgebras of noncommutative Poisson boundaries for higher rank lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Shuoxing Zhou","submitted_at":"2026-07-02T17:20:11Z","abstract_excerpt":"Let $G$ be a real connected semisimple Lie group with trivial center, no non-trivial compact factors, and all simple factors of real rank at least two. Let $\\Gamma<G$ be an irreducible lattice, let $P<G$ be a minimal parabolic subgroup, and consider the crossed product $L^\\infty(G/P,\\nu_P)\\rtimes \\Gamma$. We prove that every $\\Gamma$-invariant von Neumann subalgebra of $L^\\infty(G/P,\\nu_P)\\rtimes \\Gamma$ is of the form $L^\\infty(G/Q,\\nu_Q)\\rtimes \\Lambda$, where $P\\leq Q\\leq G$ and $\\Lambda\\lhd\\Gamma$. This confirms a conjecture of Amrutam--Hartman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02450","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.02450/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}