{"paper":{"title":"The Lattice Structure of Connection Preserving Deformations for q-Painlev\\'e Equations I","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Christopher M. Ormerod","submitted_at":"2010-10-14T22:06:46Z","abstract_excerpt":"We wish to explore a link between the Lax integrability of the $q$-Painlev\\'e equations and the symmetries of the $q$-Painlev\\'e equations. We shall demonstrate that the connection preserving deformations that give rise to the $q$-Painlev\\'e equations may be thought of as elements of the groups of Schlesinger transformations of their associated linear problems. These groups admit a very natural lattice structure. Each Schlesinger transformation induces a B\\\"acklund transformation of the $q$-Painlev\\'e equation. Each translational B\\\"acklund transformation may be lifted to the level of the asso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3036","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"}