{"paper":{"title":"The $\\mathfrak{sl}_N$ Symmetrically Large Coloured $R$ Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"primary_cat":"math.GT","authors_text":"Angus Gruen","submitted_at":"2022-12-10T06:23:18Z","abstract_excerpt":"For every knot $K$ and lie algebra $\\mathfrak{g}$, there is a Gukov-Manolescu series denoted $F^{\\mathfrak{g}}_K$ which serves as an analytic continuation of the quantum knot invariants associated to finite dimensional irreducible representations of $\\mathfrak{g}$. There has been a great deal of work done on computing this invariant for $\\mathfrak{g} = \\mathfrak{sl}_2$ but comparatively less work has studied other lie algebras. In this paper we extend the large colour $R$ matrix from $\\mathfrak{sl}_2$ to symmetrically coloured $\\mathfrak{sl}_N$. This gives a definition for $F^{\\mathfrak{sl}_N,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.05222","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/2212.05222/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"}