{"paper":{"title":"Categorical actions and multiplicities in the Deligne category $\\underline{Rep}(GL_t)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Inna Entova-Aizenbud","submitted_at":"2016-07-14T23:13:47Z","abstract_excerpt":"We study the categorical type A action on the Deligne category $\\mathcal{D}_t=\\underline{Rep}(GL_t)$ (here $t \\in \\mathbb{C}$) and its \"abelian envelope\" $\\mathcal{V}_t$ constructed in arXiv:1511.07699.\n  For $t \\in \\mathbb{Z}$, this action categorifies an action of the Lie algebra $\\mathfrak{sl}_{\\mathbb{Z}}$ on the tensor product of the Fock space $\\mathfrak{F}$ with $\\mathfrak{F}_t^{\\vee}$, its restricted dual \"shifted\" by $t$, as was suggested by I. Losev. In fact, this action makes the category $\\mathcal{V}_t$ the tensor product (in the sense of Losev and Webster, arXiv:1303.1336) of cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04341","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"}