{"paper":{"title":"The explicit Plancherel formula on the line budle of ${\\rm SL}(n+1, {\\mathbb R})/{\\rm S}({\\rm GL}(1, {\\mathbb R})\\times {\\rm GL}(n, {\\mathbb R}))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.DG","authors_text":"Liangyun Chen, Li Zhu","submitted_at":"2016-07-07T11:11:02Z","abstract_excerpt":"The purpose of this paper is to study the Plancherel formula for the spaces of $L^2$-sections of the line bundles over the pseudo-Riemannian space $G/H$, where $G={\\rm SL}(n+1, {\\mathbb R})$ and $H={\\rm S}({\\rm GL}(1, {\\mathbb R})\\times {\\rm GL}(n, {\\mathbb R}))$. The formula is given in an explicit form by means of spherical distributions associated with the character $\\chi_{_\\lambda}$ of the subgroup $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03451","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"}