{"paper":{"title":"A Characterization of Reduced Forms of Linear Differential Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.RT"],"primary_cat":"math.CA","authors_text":"Ainhoa Aparicio-Monforte, Elie Compoint, Jacques-Arthur Weil","submitted_at":"2012-06-28T12:36:24Z","abstract_excerpt":"A differential system $[A] : \\; Y'=AY$, with $A\\in \\mathrm{Mat}(n, \\bar{k})$ is said to be in reduced form if $A\\in \\mathfrak{g}(\\bar{k})$ where $\\mathfrak{g}$ is the Lie algebra of the differential Galois group $G$ of $[A]$. In this article, we give a constructive criterion for a system to be in reduced form. When $G$ is reductive and unimodular, the system $[A]$ is in reduced form if and only if all of its invariants (rational solutions of appropriate symmetric powers) have constant coefficients (instead of rational functions). When $G$ is non-reductive, we give a similar characterization vi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6661","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"}