{"paper":{"title":"Indecomposable manipulations with simple modules in category O","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kevin Coulembier, Volodymyr Mazorchuk, Xiaoting Zhang","submitted_at":"2017-09-02T09:22:52Z","abstract_excerpt":"We study the problem of indecomposability of translations of simple modules in the principal block of BGG category $\\mathcal{O}$ for $\\mathfrak{sl}_n$, as conjectured in \\cite{KiM}. We describe some general techniques and prove a few general results which may be applied to study various special cases of this problem. We apply our results to verify indecomposability for $n\\leq 6$. We also study the problem of indecomposability of shufflings and twistings of simple modules and obtain some partial results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00547","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"}