{"paper":{"title":"Toeplitz operators in TQFT via skein theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Julien March\\'e (CMLS-EcolePolytechnique), Thierry Paul (CMLS-EcolePolytechnique)","submitted_at":"2011-08-02T17:31:40Z","abstract_excerpt":"Topological quantum field theory associates to a punctured surface $\\Sigma$, a level $r$ and colors $c$ in $\\{1,...,r-1\\}$ at the marked points a finite dimensional hermitian space $V_r(\\Sigma,c)$. Curves $\\gamma$ on $\\Sigma$ act as Hermitian operator $T_r^\\gamma$ on these spaces. In the case of the punctured torus and the 4 times punctured sphere, we prove that the matrix elements of $T_r^\\gamma$ have an asymptotic expansion in powers of $\\frac{1}{r}$ and we identify the two first terms using trace functions on representation spaces of the surface in $\\su$. We conjecture a formula for the gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0629","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"}