{"paper":{"title":"Bethe algebras for unitarizable modules over classical Lie (super)algebras and a duality","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":"2025-05-26T08:20:09Z","abstract_excerpt":"Let $\\mathfrak{g}$ denote the classical Lie algebra $\\mathfrak{gl}_d$, $\\mathfrak{sp}_{2d}$, or $\\mathfrak{so}_{2d}$ with a fixed $*$-structure $\\sigma$. Let $M_1, \\ldots, M_\\ell$ be unitarizable $\\mathfrak{g}$-modules (with respect to $\\sigma$), and let ${\\bf z}=(z_1, \\ldots, z_\\ell) \\in \\mathbb{C}^\\ell$. We investigate the action of the Bethe algebra $\\mathcal{B}_{\\mathfrak{g}}^\\mu$ for $\\mathfrak{g}$ with respect to $\\mu \\in \\mathfrak{g}^*$ on the tensor product $\\underline{M}({\\bf z}):=M_1(z_1) \\otimes \\cdots \\otimes M_\\ell(z_\\ell)$ of evaluation $\\mathfrak{g}[t]$-modules. We show that if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19661","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.19661/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"}