{"paper":{"title":"Dualities for spin representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hans Wenzl","submitted_at":"2020-05-22T17:47:38Z","abstract_excerpt":"Let $S$ be the spinor representation of $U_q\\mathfrak{so}_N$, for $N$ odd and $q^2$ not a rooot of unity. We show that the commutant of its action on $S^{\\otimes n}$ is given by a representation of the nonstandard quantum group $U'_{-q^2}\\mathfrak{so}_n$. For $N$ even, an analogous statement also holds for $S=S_+\\oplus S_-$ the direct sum of the irreducible spinor representations of $U'_q\\mathfrak{so}_N$, with the commutant given by $U'_{-q}\\mathfrak{o}_n$, a $\\mathbb{Z}/2$-extension of $U'_{-q}\\mathfrak{so}_n$. Similar statements also hold for fusion tensor categories with $q$ a root of unity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.11299","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/2005.11299/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"}