{"paper":{"title":"A Graphical Calculus for Induction and Restriction on Temperley-Lieb Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alistair Savage","submitted_at":"2026-06-22T13:45:33Z","abstract_excerpt":"We develop a graphical calculus for induction and restriction along the Temperley-Lieb tower at a generic parameter. The main object, a diagrammatic 2-category $\\mathfrak{D}$, has one-step generators that model the usual induction and restriction bimodules and additional two-step generators that model the summands that the cup-cap idempotents cut out in the two-strand Temperley-Lieb algebra. We construct an incarnation 2-functor from $\\mathfrak{D}$ to the 2-category of Temperley-Lieb bimodules and prove a basis theorem for all 2-morphism spaces; the basis elements are indexed by bridges, a cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23340","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/2606.23340/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"}