{"paper":{"title":"$({\\mathfrak{gl}}_M, {\\mathfrak{gl}}_N)$-Dualities in Gaudin Models with Irregular Singularities","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.QA","authors_text":"Benoit Vicedo, Charles Young","submitted_at":"2017-10-24T09:33:02Z","abstract_excerpt":"We establish $({\\mathfrak{gl}}_M, {\\mathfrak{gl}}_N)$-dualities between quantum Gaudin models with irregular singularities. Specifically, for any $M, N \\in {\\mathbb Z}_{\\geq 1}$ we consider two Gaudin models: the one associated with the Lie algebra ${\\mathfrak{gl}}_M$ which has a double pole at infinity and $N$ poles, counting multiplicities, in the complex plane, and the same model but with the roles of $M$ and $N$ interchanged. Both models can be realized in terms of Weyl algebras, i.e., free bosons; we establish that, in this realization, the algebras of integrals of motion of the two model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08672","kind":"arxiv","version":3},"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"}