{"paper":{"title":"Integrable $sl(\\infty)$-modules and Category $\\mathcal O$ for $\\mathfrak{gl}(m|n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Crystal Hoyt, Ivan Penkov, Vera Serganova","submitted_at":"2017-12-02T20:59:36Z","abstract_excerpt":"We introduce and study new categories T(g,k)of integrable sl(\\infty)-modules which depend on the choice of a certain reductive subalgebra k in g=sl(\\infty). The simple objects of these categories are tensor modules as in the previously studied category, however, the choice of k provides more flexibility of nonsimple modules. We then choose k to have two infinite-dimensional diagonal blocks, and show that a certain injective object K(m|n) in T(g,k) realizes a categorical sl(\\infty)-action on the integral category O(m|n) of the Lie superalgebra gl(m|n). We show that the socle of K(m|n) is genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00664","kind":"arxiv","version":4},"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"}