{"paper":{"title":"Tensor products of complementary series of rank one Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Genkai Zhang","submitted_at":"2014-02-12T19:48:42Z","abstract_excerpt":"We consider the tensor product $\\pi_{\\alpha}\\otimes \\pi_{\\beta}$ of complementary series representations $\\pi_{\\alpha}$ and $\\pi_{\\beta}$ of classical rank one groups $SO_0(n, 1)$, $SU(n, 1)$ and $Sp(n, 1)$. We prove that there is a discrete component $\\pi_{\\alpha+\\beta}$ for small parameters $\\alpha, \\beta$ (in our parametrization). We prove further that for $G=SO_0(n, 1)$ there are finitely many complementary series of the form $\\pi_{\\alpha+\\beta + 2j}$, $j=0, 1, \\cdots, k$, appearing in the tensor product $\\pi_{\\alpha} \\otimes \\pi_{\\beta} $ of two complementary series $\\pi_{\\alpha}$ and $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2950","kind":"arxiv","version":4},"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"}