{"paper":{"title":"Factorization of Combinatorial R matrices and Associated Cellular Automata","license":"","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.QA","authors_text":"Atsuo Kuniba, Goro Hatayama, Taichiro Takagi","submitted_at":"2000-03-25T07:11:10Z","abstract_excerpt":"Solvable vertex models in statistical mechanics give rise to soliton cellular automata at q=0 in a ferromagnetic regime. By means of the crystal base theory we study a class of such automata associated with non-exceptional quantum affine algebras U'_q(\\hat{\\geh}_n). Let B_l be the crystal of the U'_q(\\hat{\\geh}_n)-module corresponding to the l-fold symmetric fusion of the vector representation. For any crystal of the form B = B_{l_1} \\otimes ... \\otimes B_{l_N}, we prove that the combinatorial R matrix B_M \\otimes B \\xrightarrow{\\sim} B \\otimes B_M is factorized into a product of Weyl group op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0003161","kind":"arxiv","version":3},"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"}