{"paper":{"title":"Simple Lie algebras and topological ODEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP"],"primary_cat":"math-ph","authors_text":"Boris Dubrovin, Di Yang, Marco Bertola","submitted_at":"2015-08-15T16:34:33Z","abstract_excerpt":"For a simple Lie algebra $\\mathfrak g$ we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of $\\mathfrak g$-type. The dimension of the space of solutions regular at infinity is equal to the rank of the Lie algebra. For the simplest example $\\mathfrak g=sl_2(\\mathbb C)$ the regular solution can be expressed via products of Airy functions and their derivatives; this matrix valued function was used in our previous work for computing logarithmic derivatives of the Witten - Kontsevich tau-function. For an arbitrary simple Lie algebra we construct a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03750","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"}