{"paper":{"title":"Vacuum curves of elliptic L-operators and representations of Sklyanin algebra","license":"","headline":"","cross_cats":["hep-th","nlin.SI"],"primary_cat":"solv-int","authors_text":"A.Zabrodin, I.Krichever","submitted_at":"1998-01-22T20:03:38Z","abstract_excerpt":"An algebro-geometric approach to representations of Sklyanin algebra is proposed. To each 2 \\times 2 quantum L-operator an algebraic curve parametrizing its possible vacuum states is associated. This curve is called the vacuum curve of the L-operator. An explicit description of the vacuum curve for quantum L-operators of the integrable spin chain of XYZ type with arbitrary spin $\\ell$ is given. The curve is highly reducible. For half-integer $\\ell$ it splits into $\\ell +{1/2}$ components isomorphic to an elliptic curve. For integer $\\ell$ it splits into $\\ell$ elliptic components and one ratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9801022","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"}