{"paper":{"title":"Fundaments of Quaternionic Clifford Analysis III: Fischer Decomposition in Symplectic Harmonic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.CA","authors_text":"David Eelbode, Fred Brackx, Hennie De Schepper, Roman Lavicka, Vladimir Soucek","submitted_at":"2014-04-14T15:46:27Z","abstract_excerpt":"In the framework of quaternionic Clifford analysis in Euclidean space $\\mathbb{R}^{4p}$, which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so--called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp$(p)$. Its Howe dual partner is determined to be $\\mathfrak{sl}(2,\\mathbb{C}) \\oplus \\mathfrak{sl}(2,\\mathbb{C}) = \\mathfrak{so}(4,\\mathbb{C})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3625","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"}