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We also discuss invariance properties of $\\Delta_{\\nu,\\mu}$ and give some of their explicit spectral p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.04920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-05-14T06:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"40b34bfc36fdcbad89ce19aaa03f87d783e43919e576dbaa9a6e976260ccab49","abstract_canon_sha256":"b86ee925f768262e788327b2c3463fb6c2d62370ea5e299f4b9e173413d1d2ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:34.343784Z","signature_b64":"MH+A6pu4j5K4RxnbxuBSmAuNkiY1+5vPdXvRJ/p5nlvGowgWKVC3KB7xHSNwUI63PMaens2mngIB95VxhSfSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47efc147343be10cd8639936d60bf3ba86938878820518aa851f61a6a30282a3","last_reissued_at":"2026-05-18T00:44:34.343184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:34.343184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $H_{2n+1}$. 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