{"paper":{"title":"Separable representations, KMS states, and wavelets for higher-rank graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Carla Farsi, Elizabeth Gillaspy, Judith Packer, Sooran Kang","submitted_at":"2015-05-03T22:11:15Z","abstract_excerpt":"Let $\\Lambda$ be a strongly connected, finite higher-rank graph. In this paper, we construct representations of $C^*(\\Lambda)$ on certain separable Hilbert spaces of the form $L^2(X,\\mu)$, by introducing the notion of a $\\Lambda$-semibranching function system (a generalization of the semibranching function systems studied by Marcolli and Paolucci). In particular, when $\\Lambda$ is aperiodic, we obtain a faithful representation of $C^*(\\Lambda)$ on $L^2(\\Lambda^\\infty, M)$, where $M$ is the Perron-Frobenius probability measure on the infinite path space $\\Lambda^\\infty$ recently studied by an H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00485","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"}