{"paper":{"title":"Interpolation of the oscillator representation and Azumaya algebras in tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Andrew Snowden","submitted_at":"2024-08-01T02:06:03Z","abstract_excerpt":"Let $\\mathfrak{C}$ be a symmetric tensor category and let $A$ be an Azumaya algebra in $\\mathfrak{C}$. Assuming a certain invariant $\\eta(A) \\in \\mathrm{Pic}(\\mathfrak{C})[2]$ vanishes, and fixing a certain choice of signs, we show that there is a universal tensor functor $\\Phi \\colon \\mathfrak{C} \\to \\mathfrak{D}$ for which $\\Phi(A)$ splits. We apply this when $\\mathfrak{C}=\\underline{\\mathrm{Rep}}(\\mathbf{Sp}_t(\\mathbf{F}_q))$ is the interpolation category of finite symplectic groups and $A$ is a certain twisted group algbera in $\\mathfrak{C}$, and we show that the splitting category $\\mathf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.00233","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/2408.00233/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"}