{"paper":{"title":"Two variations on $(A_3\\times A_1\\times A_1)^{(1)}$ type discrete Painlev\\'e equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Yang Shi","submitted_at":"2019-04-10T01:04:36Z","abstract_excerpt":"By considering the normalizers of reflection subgroups of types $A_1^{(1)}$ and $A_3^{(1)}$ in $\\widetilde{W}\\left(D_5^{(1)}\\right)$, two normalizers: $\\widetilde{W}\\left(A_3\\times A_1\\right)^{(1)}\\ltimes {W}(A_1^{(1)})$ and $\\widetilde{W}\\left(A_1\\times A_1\\right)^{(1)}\\ltimes {W}(A_3^{(1)})$ can be constructed from a $(A_{3}\\times A_1\\times A_1)^{(1)}$ type subroot system. These two symmetries arose in the studies of discrete \\Pa equations \\cite{KNY:2002, Takenawa:03, OS:18}, where certain non-translational elements of infinite order were shown to give rise to discrete \\Pa equations. We clar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04958","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"}