{"paper":{"title":"Solutions of bigraded Toda hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Chuanzhong Li","submitted_at":"2010-11-21T18:04:52Z","abstract_excerpt":"The $(N,M)$-bigraded Toda hierarchy is an extension of the original Toda lattice hierarchy. The pair of numbers $(N,M)$ represents the band structure of the Lax matrix which has $N$ upper and $M$ lower diagonals, and the original one is referred to as the $(1,1)$-bigraded Toda hierarchy.\n  Because of this band structure, one can introduce $M+N-1$ commuting flows which give a parametrization of a small phase space for a topological field theory.\n  In this paper, we first show that there exists a natural symmetry between the $(N,M)$- and $(M,N)$-bigraded Toda hierarchies. We then derive the Hiro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4684","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"}