{"paper":{"title":"Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Birgit Speh, Genkai Zhang","submitted_at":"2013-04-10T07:41:22Z","abstract_excerpt":"We consider the spherical complementary series of rank one Lie groups $H_n=\\SO_0(n, 1; \\mathbb F)$ for $\\mathbb F=\\mathbb R, \\mathbb C, \\mathbb H$. We prove that there exist finitely many discrete components in its restriction under the subgroup $H_{n-1}=\\SO_0(n-1, 1; \\mathbb F)$. This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of $G_n=SU(n, 1)$, $SU(n, 1)\\times SU(n, 1)$ and $SU(2n, 2)$ and by the branching of holomorphic representations under the corresponding subgroup\n  $G_{n-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2868","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"}