{"paper":{"title":"Shading A-polynomials via huge representations of $U_q(\\mathfrak{su}_N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GN","math.MP","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Alexei Morozov, Dmitry Galakhov","submitted_at":"2026-05-21T14:42:19Z","abstract_excerpt":"Classical A-polynomials $A(\\ell,m)$ define constraints on coordinates $\\ell$ and $m$ in $SL(2,\\mathbb{C})$ (a complexification of $SU(2)$) character varieties associated to knot complements $S^3\\setminus K$. Quantum A-polynomials $\\hat A(\\hat \\ell,\\hat m)$ are difference operators annihilating Jones polynomials believed to represent wave functions of 3d Chern-Simons theory with gauge group $SU(2)$ on a toroidal pipe surrounding the knot $K$ strand -- a boundary of the knot complements $S^3\\setminus K$. We suggest a construction of classical shaded A-polynomials $A_a(\\ell_b,m_c)$ associated to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22560","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/2605.22560/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"}