{"paper":{"title":"Associated symmetric pair and multiplicities of admissible restriction of Discrete Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jorge A. Vargas","submitted_at":"2013-11-15T13:52:42Z","abstract_excerpt":"Let $(G, H)$ be a symmetric pair for a real semisimple Lie group $G$ and $(G, H_0)$ its associated pair. For each irreducible square integrable representation $\\pi$ of $G$ so that its restriction to $H$ is admissible, we find an irreducible square integrable representation $\\pi_0$ of $H_0$ which allows to compute the Harish-Chandra parameter of each irreducible $H-$subrepresentation of $\\pi$ as well as its multiplicity. The computation is based on the spectral analysis of the restriction of $\\pi_0$ to a maximal compact subgroup of $H_0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3851","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"}