{"paper":{"title":"Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Atsuo Kuniba, Masato Okado, Shouya Maruyama","submitted_at":"2016-02-15T06:58:33Z","abstract_excerpt":"We consider a three-dimensional (3D) lattice model associated with the intertwiner of the quantized coordinate ring $A_q(sl_3)$, and introduce a family of layer to layer transfer matrices on $m\\times n$ square lattice. By using the tetrahedron equation we derive their commutativity and bilinear relations mixing various boundary conditions. At $q=0$ and $m=n$, they lead to a new proof of the steady state probability of the $n$-species totally asymmetric zero range process obtained recently by the authors, revealing the 3D integrability in the matrix product construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04574","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"}