Fundaments of Quaternionic Clifford Analysis III: Fischer Decomposition\n in Symplectic Harmonic Analysis

2014/04/14 by Fred Brackx, Brackx, Fred, Hennie De Schepper +8
Mathematics · #35J05 31B05 30G35 22E60 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1404.3625

openalex publication_date 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the framework of quaternionic Clifford analysis in Euclidean space\n\ℝ^4p, which constitutes a refinement of Euclidean and Hermitian\nClifford analysis, the Fischer decomposition of the space of complex valued\npolynomials is obtained in terms of spaces of so--called (adjoint) symplectic\nspherical harmonics, which are irreducible modules for the symplectic group\nSp(p). Its Howe dual partner is determined to be mathfraksl(2,\ℂ)\n\⊕ mathfraksl(2,\ℂ) = mathfrakso(4,\ℂ).\n

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