{"paper":{"title":"Unitary Representations of Lie Groups with Reflection Symmetry","license":"","headline":"","cross_cats":["math.FA","math.RT"],"primary_cat":"funct-an","authors_text":"Gestur \\'Olafsson, Palle E.T. Jorgensen","submitted_at":"1997-07-11T17:04:50Z","abstract_excerpt":"We consider the following class of unitary representations $\\pi $ of some (real) Lie group $G$ which has a matched pair of symmetries described as follows: (i) Suppose $G$ has a period-2 automorphism $\\tau $, and that the Hilbert space $\\mathbf{H} (\\pi)$ carries a unitary operator $J$ such that $J\\pi =(\\pi \\circ \\tau)J$ (i.e., selfsimilarity). (ii) An added symmetry is implied if $\\mathbf{H} (\\pi)$ further contains a closed subspace $\\mathbf{K}_0 $ having a certain order-covariance property, and satisfying the $\\mathbf{K}_0 $-restricted positivity: $< v \\mid Jv > \\ge 0$, $\\forall v\\in \\mathbf{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9707001","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"}