{"paper":{"title":"The Gaudin model for the general linear Lie superalgebra and the completeness of the Bethe ansatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Ngau Lam, Wan Keng Cheong","submitted_at":"2024-12-31T11:40:54Z","abstract_excerpt":"Let $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})$ be the Gaudin algebra of the general linear Lie superalgebra $\\mathfrak{gl}_{m|n}$ with respect to a sequence $\\underline{\\boldsymbol{z}} \\in \\mathbb{C}^\\ell$ of pairwise distinct complex numbers, and let $M$ be any $\\ell$-fold tensor product of irreducible polynomial modules over $\\mathfrak{gl}_{m|n}$. We show that the singular space $M^{\\rm sing}$ of $M$ is a cyclic $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})$-module and the Gaudin algebra $\\mathfrak{B}_{m|n}(\\underline{\\boldsymbol{z}})_{M^{\\rm sing}}$ of $M^{\\rm sing}$ is a Frobenius "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.00401/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"}