{"paper":{"title":"Type $B$ Webs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Ben Elias, David E. V. Rose, Elijah Bodish","submitted_at":"2026-07-14T20:34:31Z","abstract_excerpt":"We solve the type $B$ case of the main open problem from Kuperberg's 1996 paper \"Spiders for rank 2 Lie algebras.\" That is, we define a $\\mathbb{C}(q)$-linear pivotal category $\\mathbf{Web}(\\mathfrak{so}_{2n+1})$ and prove that it is equivalent to the full subcategory of finite-dimensional representations of $U_q(\\mathfrak{so}_{2n+1})$ tensor-generated by the fundamental representations. A consequence of our main result is an explicit construction of braid group symmetries for nonclassical finite-dimensional representations of the $\\iota$quantum group ${U}^{\\iota}_{-q^2}(\\mathfrak{so}_m)$, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13252","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/2607.13252/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"}