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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.00233","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-08-01T02:06:03Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"7b8f3d4b73de2eefa4c54e68e111b25949856fcb38d5833a8ad6e2f8e897a7d3","abstract_canon_sha256":"5ae8b7075577d18a85ddd8f92b9bb5a39996b43ea4099557ac7b2e6a0ff2dd1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:51:00.319808Z","signature_b64":"tW3bK1X1L3hah8Q/dTkkggFyE6uSti87R6KBwPyf5Fz453cbWvLteColKu6t5d6b8MCYOL3q2REEGyqpoprbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a47ab61a165457da536081824bf7f14f4559c8efd46bb4b502290e636090167","last_reissued_at":"2026-07-05T08:51:00.319365Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:51:00.319365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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