{"paper":{"title":"Discrete components in restriction 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":"Genkai Zhang","submitted_at":"2011-11-28T11:14:21Z","abstract_excerpt":"We consider spherical principal series representations of the semisimple Lie group of rank one $G=SO(n, 1; \\mathbb K)$, $\\mathbb K=\\br, \\bc, \\bh$. There is a family of unitarizable representations $\\pi_{\\nu}$ of $G$ for $\\nu$ in an interval on $\\mathbb R^+$, the so-called complementary series, and subquotient or subrepresentations of $G$ for $\\nu$ being negative integers. We consider the restriction of $(\\pi_{\\nu}, G)$ under the subgroup $H=SO(n-1, 1; \\mathbb K)$. We prove the appearing of discrete components. The corresponding results for the exceptional Lie group $F_{4(-20)}$ and its subgrou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6406","kind":"arxiv","version":3},"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"}