{"paper":{"title":"Symmetry breaking for representations of rank one orthogonal groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NT"],"primary_cat":"math.RT","authors_text":"Birgit Speh, Toshiyuki Kobayashi","submitted_at":"2017-12-30T17:26:41Z","abstract_excerpt":"For a pair $(G,G')=(O(n+1,1), O(n,1))$ of reductive groups, we investigate intertwining operators (symmetry breaking operators) between principal series representations $I_\\delta(V,\\lambda)$ of $G$, and $J_\\epsilon(W,\\nu)$ of the subgroup $G'$. The representations are parametrized by finite-dimensional representations $V,W$ of $O(n)$ respectively of $O(n-1)$, characters $\\delta$, $\\varepsilon$ of O(1), and $\\lambda, \\nu \\in C$.\n  The multiplicty [V:W] of W occurring in the restriction $V|_{O(n-1)}$ is either 0 or 1. If $[V:W] \\ne 0$ then we construct a holomorphic family of symmetry breaking o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00158","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"}