{"paper":{"title":"On the dual topology of the groups U(n)xH_n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Janne-Kathrin G\\\"unther, Jean Ludwig, Mounir Elloumi","submitted_at":"2017-02-13T12:48:30Z","abstract_excerpt":"Let $G_n=U(n)\\ltimes {\\mathbb H}_n $ be the semi-direct product of the unitary group acting by automorphisms on the Heisenberg group ${\\mathbb H}_n$. According to Lipsman, the unitary dual $\\widehat {G_n} $ of $G_n $ is in one to one correspondence with the space of admissible coadjoint orbits $\\mathfrak g_n^\\ddagger /G_n $ of $G_n $. In this paper, we determine the topology of the space $\\mathfrak g_n^\\ddagger /G_n $ and we show that the correspondence with $\\widehat {G_n} $ is a homeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03747","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"}