{"paper":{"title":"Irreducible representations of untwisted affine Kac-Moody algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kaiming Zhao, Xiangqian Guo","submitted_at":"2013-05-17T12:25:54Z","abstract_excerpt":"In this paper we construct a class of new irreducible modules over untwisted affine Kac-Moody algebras $\\widetilde{\\mathfrak{g}}$, generalizing and including both highest weight modules and Whittaker modules. These modules allow us to obtain a complete classification of irreducible $\\widetilde{\\mathfrak{g}}$-modules on which the action of each root vector in $\\widetilde{\\mathfrak{n}}_+$ is locally finite, where $\\widetilde{\\mathfrak{n}}_+$ is the locally nilpotent subalgebra (or positive part) of $\\widetilde{\\mathfrak{g}}$. The necessary and sufficient conditions for two such irreducible $\\wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4059","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":""},"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"}