{"paper":{"title":"Representing some II$_1$ factors in $L^2(\\Lambda \\backslash G)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.OA","authors_text":"Lauren C. Ruth","submitted_at":"2019-07-17T17:04:06Z","abstract_excerpt":"Let $G$ be $PGL(n,F)$, $n \\geq 3$, $F$ a certain non-archimedean local field; or let $G$ be $PSL(2,\\mathbb{R}) \\times \\cdots \\times PSL(2,\\mathbb{R})$. Let $\\Gamma$ be a lattice in $G$, and let $( \\Lambda_n )$ be a sequence of lattices in $G$ satisfying the pointwise limit multiplicity property. In this note, we explain how the pointwise limit multiplicity property can be combined with a generalization of a theorem in \\cite{ghj} to give representations of the II$_1$ factor $R \\Gamma$ on a subspace of $L^2(\\Lambda_i \\backslash G)$ for some $\\Lambda_i$ in $( \\Lambda_n )$. This extends a result i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07641","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":""},"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"}