{"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 $\\mathbb{C}$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03645","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}