{"paper":{"title":"On concrete spectral properties of a twisted-Laplacian associated to a central extension of the real Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ahmed Intissar, Allal Ghanmi, Aymane EL Fardi","submitted_at":"2017-05-14T06:34:03Z","abstract_excerpt":"We consider the magnetic Laplacian $\\Delta_{\\nu,\\mu}$ on $\\mathbb{R}^{2n}=\\mathbb{C}^n$ given by $$ \\Delta_{\\nu,\\mu}= 4\\sum\\limits_{j=1}\\limits^{n}\\frac{\\partial^2 }{\\partial z_j \\partial \\overline{z_j}} +2i\\nu (E+ \\overline{E} +n) +2\\mu (E- \\overline{E} ) -(\\nu^2+\\mu^2)|z|^2. $$ We show that $\\Delta_{\\nu,\\mu}$ is connected to the sub-Laplacian of a group of Heisenberg type given by $\\mathbb{C}\\times_\\omega \\mathbb{C}^n$ realized as a central extension of the real Heisenberg group $H_{2n+1}$. We also discuss invariance properties of $\\Delta_{\\nu,\\mu}$ and give some of their explicit spectral p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04920","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"}