{"paper":{"title":"The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Adam Doliwa","submitted_at":"2010-06-17T06:26:06Z","abstract_excerpt":"We study recently introduced Desargues maps, which provide simple geometric interpretation of the non-commutative Hirota--Miwa system. We characterize them as maps of the A-type root lattice into a projective space such that images of vertices of any basic regular N-simplex are collinear. Such a characterization is manifestly invariant with respect to the corresponding affine Weyl group action, which leads to related symmetries of the Hirota--Miwa system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3380","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"}