{"paper":{"title":"The duality of $\\mathfrak{gl}_{m|n}$ and $\\mathfrak{gl}_k$ Gaudin models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Chenliang Huang, Evgeny Mukhin","submitted_at":"2019-04-04T19:09:57Z","abstract_excerpt":"We establish a duality of the non-periodic Gaudin model associated with superalgebra $\\mathfrak{gl}_{m|n}$ and the non-periodic Gaudin model associated with algebra $\\mathfrak{gl}_k$.\n  The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an $(m+n)\\times(m+n)$ matrix in the case of $\\mathfrak{gl}_{m|n}$ and of a column determinant of a $k\\times k$ matrix in the case of $\\mathfrak{gl}_k$. We obtain our results by proving Capelli type identities for both cases and comparing the results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02753","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":""},"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"}