{"paper":{"title":"$BC_2$ type multivariable matrix functions and matrix spherical functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Erik Koelink, Jie Liu","submitted_at":"2021-10-05T18:51:34Z","abstract_excerpt":"Matrix spherical functions associated to the compact symmetric pair $(\\mathrm{SU}(m+2), \\mathrm{S}(\\mathrm{U}(2)\\times \\mathrm{U}(m))$, having reduced root system of type $\\mathrm{BC}_2$, are studied. We consider an irreducible $K$-representation $(\\pi,V)$ arising from the $\\mathrm{U}(2)$-part of $K$, and the induced representation $\\mathrm{Ind}_K^G \\pi$ splits multiplicity free. The corresponding spherical functions, i.e. $\\Phi \\colon G \\to \\mathrm{End}(V)$ satisfying $\\Phi(k_1gk_2)=\\pi(k_1)\\Phi(g)\\pi(k_2)$ for all $g\\in G$, $k_1,k_2\\in K$, are studied by studying certain leading coefficients"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.02287","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.02287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}