{"paper":{"title":"The Matrix Bochner Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CA"],"primary_cat":"math.RA","authors_text":"Milen Yakimov, W. Riley Casper","submitted_at":"2018-03-12T17:58:53Z","abstract_excerpt":"A long standing question in the theory of orthogonal matrix polynomials is the matrix Bochner problem, the classification of $N \\times N$ weight matrices $W(x)$ whose associated orthogonal polynomials are eigenfunctions of a second order differential operator. Based on techniques from noncommutative algebra (semiprime PI algebras of Gelfand-Kirillov dimension one), we construct a framework for the systematic study of the structure of the algebra $\\mathcal D(W)$ of matrix differential operators for which the orthogonal polynomials of the weight matrix $W(x)$ are eigenfunctions. The ingredients "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04405","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"}