{"paper":{"title":"Funciones Esf\\'ericas Matriciales Asociadas a las Esferas y a los Espacios Proyectivos Reales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ignacio N. Zurri\\'an","submitted_at":"2013-06-27T17:31:25Z","abstract_excerpt":"In this work we start by determining all irreducible spherical functions $\\Phi$ of any $K $-type associated to the pair $(G,K)=(\\SO(4),\\SO(3))$. The functions $P=P(u)$ corresponding to the irreducible spherical functions of a fixed $K$-type $\\pi_\\ell$ are appropriately packaged into a sequence of matrix valued polynomials $(P_w)_{w\\ge0}$ of size $(\\ell+1)\\times(\\ell+1)$. Finally we prove that $\\widetilde P_w={P_0}^{-1}P_w$ is a sequence of matrix orthogonal polynomials with respect to a weight matrix $W$. Moreover, we show that $W$ admits a second order symmetric hypergeometric operator $\\wide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6581","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"}