{"paper":{"title":"Integrable Hierarchy for Multidimensional Toda Equations and Topological-Anti-topological Fusion","license":"","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"hep-th","authors_text":"A.H. Zimerman, H. Aratyn, J.F. Gomes","submitted_at":"2001-07-06T17:46:30Z","abstract_excerpt":"The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous $A_m$-hierarchy and its $\\hat{gl} (m+1, C)$ extension. A loop group automorphism of order two is used to define a sub-hierarchy of $\\hat{gl} (m+1, C)$ hierarchy containing only the odd symmetry flows. The positive and negative flows of the $\\pm 1$ grade coincide with equations of the multidimensional Toda model and of topological-anti-topological fusion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0107056","kind":"arxiv","version":3},"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"}