{"paper":{"title":"Shintani functions, real spherical manifolds, and symmetry breaking operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.RT","authors_text":"Toshiyuki Kobayashi","submitted_at":"2013-12-31T09:25:25Z","abstract_excerpt":"For a pair of reductive groups $G \\supset G'$, we prove a geometric criterion for the space $Sh(\\lambda, \\nu)$ of Shintani functions to be finite-dimensional in the Archimedean case.\n  This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces.\n  A geometric criterion for uniform boundedness of $dim Sh(\\lambda, \\nu)$ is also obtained.\n  Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible representations yield Shintani functions of moderate growth, of which the dimension is determined "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0117","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"}