{"paper":{"title":"The dual pair $\\big(U_q(\\mathfrak{su}(1,1)),\\mathfrak{o}_{q^{1/2}}(2n)\\big)$, $q$-oscillators and Askey-Wilson algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Ragoucy, Julien Gaboriaud, Luc Frappat, Luc Vinet","submitted_at":"2019-08-12T17:39:23Z","abstract_excerpt":"The universal Askey-Wilson algebra $AW(3)$ can be obtained as the commutant of $U_q(\\mathfrak{su}(1,1))$ in $U_q(\\mathfrak{su}(1,1))^{\\otimes3}$. We analyze the commutant of $\\mathfrak{o}_{q^{1/2}}(2)\\oplus\\mathfrak{o}_{q^{1/2}}(2)\\oplus\\mathfrak{o}_{q^{1/2}}(2)$ in $q$-oscillator representations of $\\mathfrak{o}_{q^{1/2}}(6)$ and show that it also realizes $AW(3)$. These two pictures of $AW(3)$ are shown to be dual in the sense of Howe; this is made clear by highlighting the role of the intermediate Casimir elements of each members of the dual pair $\\big(U_q(\\mathfrak{su}(1,1)),\\mathfrak{o}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04277","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/1908.04277/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"}