{"paper":{"title":"Quantizations on Nilpotent Lie Groups and Algebras Having Flat Coadjoint Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"M. Mantoiu, M. Ruzhansky","submitted_at":"2016-11-22T23:47:26Z","abstract_excerpt":"For a connected simply connected nilpotent Lie group $\\G$ with Lie algebra $\\g$ and unitary dual $\\wG$ one has (a) a global quantization of operator-valued symbols defined on $\\G\\times\\wG$, involving the representation theory of the group, (b) a quantization of scalar-valued symbols defined on $\\G\\times\\g^*$, taking the group structure into account and (c) Weyl-type quantizations of all the coadjoint orbits $\\big\\{\\O_\\xi\\mid\\xi\\in\\wG\\big\\}$. We show how these quantizations are connected, in the case when flat coadjoint orbits exist. This is done by a careful analysis of the composition of two "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07581","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"}