{"paper":{"title":"Irreducible decomposition for local representations of quantum Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Toulisse J\\'er\\'emy","submitted_at":"2014-04-19T08:40:43Z","abstract_excerpt":"We give an irreducible decomposition of the so-called local representations (see arXiv:0707.2151) of the quantum Teichm\\\"uller space $\\mathcal{T}_q(\\Sigma)$ where $\\Sigma$ is a punctured surface of genus $g>0$ and $q$ is a primitive $N$-th root of unity with $N$ odd. As an application, we construct a family of representations of the Kauffman bracket skein algebra of the closed surface $\\overline\\Sigma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4938","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"}