{"paper":{"title":"The inversion formula and holomorphic extension of the minimal representation of the conformal group","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Gen Mano, Toshiyuki Kobayashi","submitted_at":"2006-06-30T23:42:06Z","abstract_excerpt":"The minimal representation $\\pi$ of the indefinite orthogonal group $O(m+1,2)$ is realized on the Hilbert space of square integrable functions on $\\mathbb R^m$ with respect to the measure $|x|^{-1} dx_1... dx_m$.\n  This article gives an explicit integral formula for the holomorphic extension of $\\pi$ to a holomorphic semigroup of $O(m+3, \\mathbb C)$ by means of the Bessel function.\n  Taking its `boundary value', we also find the integral kernel of the `inversion operator' corresponding to the inversion element on the Minkowski space $\\mathbb R^{m,1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607007","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"}