{"paper":{"title":"Iterated torus knots and double affine Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Peter Samuelson","submitted_at":"2014-08-03T10:48:47Z","abstract_excerpt":"We give a topological realization of the (spherical) double affine Hecke algebra $\\mathrm{SH}_{q,t}$ of type $A_1$, and we use this to construct a module over $\\mathrm{SH}_{q,t}$ for any knot $K \\subset S^3$. As an application, we give a purely topological interpretation of Cherednik's 2-variable polynomials $P_n(r,s; q,t)$ of type $A_1$ from [Che13] (where $r,s \\in \\mathbb{Z}$ are relatively prime), and we give a new proof that these specialize to the colored Jones polynomials of the $r,s$ torus knot.\n  We then generalize Cherednik's construction (for $\\mathcal{sl}_2$) to all iterated cables "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0483","kind":"arxiv","version":4},"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"}