{"paper":{"title":"Triangular Subgroups of $Sp(d,{\\mathbb R})$ and Reproducing Formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.RT","authors_text":"Anita Tabacco, Elena Cordero","submitted_at":"2014-02-19T09:40:47Z","abstract_excerpt":"We consider the (extended) metaplectic representation of the semidirect product $\\mathcal{G}={\\mathbb H}^d\\rtimes Sp(d,{\\mathbb R})$ between the Heisenberg group and the symplectic group. Subgroups $H=\\Sigma \\rtimes D$, with $\\Sigma$ being a $d\\times d$ symmetric matrix and $D$ a closed subgroup of $GL(d,{\\mathbb R})$, are our main concern. We shall give a general setting for the reproducibility of such groups which include and assemble the ones for the single examples treated in [5]. As a byproduct, the extended metaplectic representation restricted to some classes of such subgroups is either"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4604","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"}