{"paper":{"title":"d-orthogonal polynomials, Toda Lattice and Virasoro symmetries","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Emil Horozov","submitted_at":"2019-04-17T10:36:33Z","abstract_excerpt":"The subject of this paper is a connection between d-orthogonal polynomials and the Toda lattice hierarchy. In more details we consider some polynomial systems similar to Hermite polynomials, but satisfying $d+2$-term recurrence relation, $d >1$. Any such polynomial system defines a solution of the Toda lattice hierarchy. However we impose also the condition that the polynomials are also eigenfunctions of a differential operator, i.e. a bispectral problem. This leads to a solution of the Toda lattice hierarchy, enjoying a number of special properties. In particular the corresponding tau-functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08173","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"}