{"paper":{"title":"Spherical Harmonics $Y_{l}^{m}(\\theta,\\phi)$: Positive and Negative Integer Representations of su(1,1) for l-m and l+m","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"H. Fakhri","submitted_at":"2016-02-25T14:42:50Z","abstract_excerpt":"The azimuthal and magnetic quantum numbers of spherical harmonics $Y_{l}^{m}(\\theta,\\phi)$ describe quantization corresponding to the magnitude and $z$-component of angular momentum operator in the framework of realization of $su(2)$ Lie algebra symmetry. The azimuthal quantum number $l$ allocates to itself an additional ladder symmetry by the operators which are written in terms of $l$. Here, it is shown that simultaneous realization of the both symmetries inherits the positive and negative $(l-m)$- and $(l+m)$-integer discrete irreducible representations for $su(1,1)$ Lie algebra via the sph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07951","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"}