{"paper":{"title":"Fischer Decomposition for osp(4|2)-monogenics in Quaternion Clifford Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.RT"],"primary_cat":"math.CV","authors_text":"David Eelbode, Fred Brackx, Hennie De Schepper, Roman Lavicka, Vladimir Soucek","submitted_at":"2015-06-18T11:37:34Z","abstract_excerpt":"Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp$( p)$. These Fischer decompositions involve spaces of homogeneous, so-called $\\mathfrak{osp}(4|2)$-monogenic polynomials, the Lie superalgebra $\\mathfrak{osp}(4|2)$ being the Howe dual partner to the symplectic group Sp$( p)$. In order to obtain Sp$( p)$-irreducibility this new concept of $\\mathfrak{osp}(4|2)$-monogenicity has to be introduced as a refinement of quaternionic monogenicity; it is defined "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05634","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"}