{"paper":{"title":"Explicit fundamental solutions of some second order differential operators on Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Isolda Cardoso, Linda Saal","submitted_at":"2012-05-24T15:46:05Z","abstract_excerpt":"Let $p,q,n$ be natural numbers such that $p+q=n$. Let $\\FF$ be either $\\CC$, the complex numbers field, or $\\HH$, the quaternionic division algebra. We consider the Heisenberg group $N(p,q,\\FF)$ defined as $N(p,q,\\FF)=\\FF^{n}\\times \\mathfrak{Im}\\FF$, with group law given by $$(v,\\zeta)(v',\\zeta')=(v+v', \\zeta+\\zeta'-{1/2} \\mathfrak{Im} B(v,v')),$$ where $B(v,w)=\\sum_{j=1}^{p} v_{j}\\bar{w_{j}} - \\sum_{j=p+1}^{n} v_{j}\\bar{w_{j}}$. Let $U(p,q,\\FF)$ be the group of $n\\times n$ matrices with coefficients in $\\FF$ that leave invariant the form $B$. In this work we compute explicit fundamental solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5489","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"}