{"paper":{"title":"Lie Groups of Jacobi polynomials and Wigner d-matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"E. Celeghini, M.A. del Olmo, M.A. Velasco","submitted_at":"2014-02-21T06:57:40Z","abstract_excerpt":"A symmetry $SU(2,2)$ group in terms of ladder operators is presented for the Jacobi polynomials, $J_{n}^{(\\alpha,\\beta)}(x)$, and the Wigner $d_j$-matrices where the spins $j=n+(\\alpha+\\beta)/2$ integer and half-integer are considered together. A unitary irreducible representation of $SU(2,2)$ is constructed and subgroups of physical interest are discussed.\n  The Universal Enveloping Algebra of $su(2,2)$ also allows to construct group structures $(SU(1,1), SO(3,2), Spin(3,2))$ whose representations separate integers and half-integers values of the spin $j$.\n  Appropriate $L^2$--functions space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5217","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"}