{"paper":{"title":"Baxter operator and Baxter equation for $q$-Toda and Toda$_2$ chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"K.K. Kozlowski, O. Babelon, V. Pasquier","submitted_at":"2018-03-16T12:44:31Z","abstract_excerpt":"We construct the Baxter operator $\\boldsymbol{ \\texttt{Q} }(\\lambda)$ for the $q$-Toda chain and the Toda$_2$ chain (the Toda chain in the second Hamiltonian structure). Our construction builds on the relation between the Baxter operator and B\\\"acklund transformations that were unravelled in {\\cite{GaPa92}}. We construct a number of quantum intertwiners ensuring the commutativity of $\\boldsymbol{ \\texttt{Q} }(\\lambda)$ with the transfer matrix of the models and the one of $\\boldsymbol{ \\texttt{Q} }$'s between each other. Most importantly, $\\boldsymbol{ \\texttt{Q} }(\\lambda)$ is modular invaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06196","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"}