{"paper":{"title":"Subalgebras of $\\gc_N$ and Jacobi polynomials","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alberto De Sole, Victor G. Kac","submitted_at":"2001-12-13T17:45:18Z","abstract_excerpt":"We classify the subalgebras of the general Lie conformal algebra $\\gc_N$ that act irreducibly on $\\C[\\partial]^N$ and that are normalized by the $\\operatorname{sl}_2$--part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials $P_n^{(-\\sigma,\\sigma)}$, $\\sigma\\in\\C$. The connection goes both ways -- we use in our classification some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0112028","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"}