{"paper":{"title":"The $q$-Higgs 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":"2019-03-11T21:40:11Z","abstract_excerpt":"A $q$-analogue of the Higgs algebra, which describes the symmetry properties of the harmonic oscillator on the $2$-sphere, is obtained as the commutant of the $\\mathfrak{o}_{q^{1/2}}(2) \\oplus \\mathfrak{o}_{q^{1/2}}(2)$ subalgebra of $\\mathfrak{o}_{q^{1/2}}(4)$ in the $q$-oscillator representation of the quantized universal enveloping algebra $U_q(\\mathfrak{u}(4))$. This $q$-Higgs algebra is also found as a specialization of the Askey--Wilson algebra embedded in the tensor product $U_q(\\mathfrak{su}(1,1))\\otimes U_q(\\mathfrak{su}(1,1))$. The connection between these two approaches is establish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04616","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/1903.04616/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"}