{"paper":{"title":"Quantum Group Theory in $\\tau^{(2)}$-model, Duality of $\\tau^{(2)}$-model and XXZ-model with Cyclic ${\\bf U_q(sl_2)}$-representation for ${\\bf q^n =1}$, and Chiral Potts Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Shi-shyr Roan","submitted_at":"2012-06-19T23:03:55Z","abstract_excerpt":"We identify the quantum group ${\\Large\\textsl{U}}_\\textsl{w}(sl_2)$ in the $L$-operator of $\\tau^{(2)}$-model for a generic $\\textsl{w}$ as a subalgebra of $U_{\\sf q} (sl_2)$ with $\\textsl{w} = {\\sf q}^{-2}$. In the roots of unity case, ${\\sf q}=q, \\textsl{w} = \\omega$ with $q^{{\\bf n}} = \\omega^N = 1$, the eigenvalues and eigenvectors of XXZ-model with the $U_q (sl_2)$-cyclic representation are determined by the $\\tau^{(2)}$-model with the induced ${\\Large\\textsl{U}}_\\omega(sl_2)$-cyclic representation, which is decomposed as a finite sum of $\\tau^{(2)}$-models in non-superintegrable inhomoge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4356","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"}