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One is the symmetric monoidal category ${\\rm Rep}(S_{\\infty})$ of algebraic representations of the infinite symmetric group $S_{\\infty} = \\bigcup_n S_n$, related to the theory of ${\\bf FI}$-modules. The other is the family of rigid symmetric monoidal Deligne categories $\\underline{{\\rm Rep}}(S_t)$, $t \\in \\mathbb{C}$, together with their abelian versions $\\underline{{\\rm Rep}}^{ab}(S_t)$, constructed by Comes and Ostrik.\n  We show that for any $t \\in \\mathbb{C}$ the natu"},"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":"1706.03645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-09T15:57:57Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"0692e85701be147ae5aae516957f907017b9bf4d793a6dd7f82d0f4ff8ebceea","abstract_canon_sha256":"ab6167ee83976fc7f10bf89946cbbb02a07f30e5514ad7be5430b1878885950e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:00.210558Z","signature_b64":"3D4UDV0bPEDhRwxJiObv/HJw17im3IFfY/fq5RqDj2aGQ0VESQcF1n6tK4YRFbCZy1qZZF572F8Ya2KJgAkaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91d237e516218b52ecfebaaa28f155f1dea64cc5497d58bc07ee6f1b73227840","last_reissued_at":"2026-05-17T23:56:00.209909Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:00.209909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deligne categories and representations of the infinite symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Daniel Barter, Inna Entova-Aizenbud, Thorsten Heidersdorf","submitted_at":"2017-06-09T15:57:57Z","abstract_excerpt":"We establish a connection between two settings of representation stability for the symmetric groups $S_n$ over $\\mathbb{C}$. 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