{"paper":{"title":"Annihilators of highest weight $\\frak{sl}(\\infty)$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"A. Petukhov, I. Penkov","submitted_at":"2014-10-30T16:34:31Z","abstract_excerpt":"We give a criterion for the annihilator in U$(\\frak{sl}(\\infty))$ of a simple highest weight $\\frak{sl}(\\infty)$-module to be nonzero. As a consequence we show that, in contrast with the case of $\\frak{sl}(n)$, the annihilator in U$(\\frak{sl}(\\infty))$ of any simple highest weight $\\frak{sl}(\\infty)$-module is integrable, i.e., coincides with the annihilator of an integrable $\\frak{sl}(\\infty)$-module. Furthermore, we define the class of ideal Borel subalgebras of $\\frak{sl}(\\infty)$, and prove that any prime integrable ideal in U$(\\frak{sl}(\\infty))$ is the annihilator of a simple $\\frak b^0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8430","kind":"arxiv","version":1},"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"}