{"paper":{"title":"Multiplicity one theorems: the Archimedean case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Binyong Sun, Chen-bo Zhu","submitted_at":"2009-03-08T13:06:53Z","abstract_excerpt":"Let $G$ be one of the classical Lie groups $\\GL_{n+1}(\\R)$, $\\GL_{n+1}(\\C)$, $\\oU(p,q+1)$, $\\oO(p,q+1)$, $\\oO_{n+1}(\\C)$, $\\SO(p,q+1)$, $\\SO_{n+1}(\\C)$, and let $G'$ be respectively the subgroup $\\GL_{n}(\\R)$, $\\GL_{n}(\\C)$, $\\oU(p,q)$, $\\oO(p,q)$, $\\oO_n(\\C)$, $\\SO(p,q)$, $\\SO_n(\\C)$, embedded in $G$ in the standard way. We show that every irreducible Casselman-Wallach representation of $G'$ occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of $G$. Similar results are proved for the Jacobi groups $\\GL_{n}(\\R)\\ltimes \\oH_{2n+1}(\\R)$, $\\GL_{n}(\\C)\\ltimes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1413","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":""},"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"}