{"paper":{"title":"Singular conformally invariant trilinear forms and covariant differential operators on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jean-Louis Clerc","submitted_at":"2011-02-09T13:43:39Z","abstract_excerpt":"Let $G=SO_0(1,n)$ be the conformal group acting on the $(n-1)$ dimensional sphere $S$, and let $(\\pi_\\lambda)_{\\lambda\\in \\mathbb C}$ be the spherical principal series. For generic values of $\\boldsymbol \\lambda =(\\lambda_1,\\lambda_2,\\lambda_3)$ in $\\mathbb C^3$, there exits a (essentially unique) trilinear form on $\\mathcal C^\\infty(S)\\times \\mathcal C^\\infty(S)\\times \\mathcal C^\\infty(S)$ which is invariant under $\\pi_{\\lambda_1}\\otimes \\pi_{\\lambda_2}\\otimes \\pi_{\\lambda_3}$. Using differential operators on the sphere $S$ which are covariant under the conformal group $SO_0(1,n)$, we constru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1861","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"}