{"paper":{"title":"Global $\\widetilde{SL(2,R)}$ representations of the Schr\\\"{o}dinger equation with time-dependent potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Jose Franco","submitted_at":"2011-04-18T15:11:45Z","abstract_excerpt":"We study the representation theory of the solution space of the one-dimensional Schr\\\"{o}dinger equation with time-dependent potentials that posses $\\mathfrak{sl}_2$-symmetry. We give explicit local intertwining maps to multiplier representations and show that the study of the solution space for potentials of the form $V(t,x)=g_2(t)x^2+g_1(t)x+g_0(t)$ reduces to the study of the potential free case. We also show that the study of the time-dependent potentials of the form $V(t,x)=\\lambda x^{-2}+g_2(t)x^2+g_0(t)$ reduces to the study of the potential $V(t,x)=\\lambda x^{-2}$. Therefore, we study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3508","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"}