{"paper":{"title":"Finite multiplicity theorems for induction and restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Toshio Oshima, Toshiyuki Kobayashi","submitted_at":"2011-08-17T13:39:27Z","abstract_excerpt":"We find upper and lower bounds of the multiplicities of irreducible admissible representations $\\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\\tau$ from irreducible representations $\\tau$ of a closed subgroup $H$.\n  As corollaries, we establish geometric criteria for finiteness of the dimension of $Hom_G(\\pi,Ind_H^G \\tau)$ (induction) and of $Hom_H(\\pi|_H,\\tau)$ (restriction) by means of the real flag variety $G/P$, and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3477","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"}