{"paper":{"title":"$\\mathcal{U}(\\mathfrak{h})$-finite modules and weight modules I: weighting functors, almost-coherent families and category $\\mathfrak{A}^{\\text{irr}}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eduardo M. Mendon\\c{c}a","submitted_at":"2024-11-27T14:32:29Z","abstract_excerpt":"This paper builds upon J. Nilsson's classification of rank one $\\mathcal{U}(\\mathfrak{h})$-free modules by extending the analysis to modules without rank restrictions, focusing on the category $\\mathfrak{A}$ of $\\mathcal{U}(\\mathfrak{h})$-finite $\\mathfrak{g}$-modules. A deeper investigation of the weighting functor $\\mathcal{W}$ and its left derived functors, $\\mathcal{W}_*$, led to the proof that simple $\\mathcal{U}(\\mathfrak{h})$-finite modules of infinite dimension are $\\mathcal{U}(\\mathfrak{h})$-torsion free. Furthermore, it is shown that these modules are $\\mathcal{U}(\\mathfrak{h})$-free"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18390","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18390/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}