{"paper":{"title":"Whittaker modules for the affine Lie algebra $A_1 ^{(1)}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Drazen Adamovic, Kaiming Zhao, Rencai Lu","submitted_at":"2014-09-18T16:02:04Z","abstract_excerpt":"We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra $\\widehat{sl_2}$ of type $A_1^{(1)}$ with noncritical level which are also irreducible Whittaker modules over $\\widetilde{sl_2} =\\widehat{sl_2} + {\\Bbb C} d $ with the same Whittaker function and central charge. We have to modulo a central character for ${sl_2}$ to obtain irreducible degenerate Whittaker $\\widehat{sl_2} $-modules with noncritical level. In the case of critical level the universal Whittaker module is reducible. We prove that the quotient of universal Whittaker $\\widehat{sl_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5354","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"}