{"paper":{"title":"Conformal Galilei algebras, symmetric polynomials and singular vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DG","math.FA","math.MP"],"primary_cat":"math.RT","authors_text":"Libor K\\v{r}i\\v{z}ka, Petr Somberg","submitted_at":"2016-12-28T14:09:52Z","abstract_excerpt":"We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras $\\mathfrak{cga}_\\ell(d,{\\mathbb C})$ with $d=1$ for any integer value $\\ell \\in \\mathbb{N}$. The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type, and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08891","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"}