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arXiv · 1404.3625

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

Fred Brackx·Hennie De Schepper·David Eelbode·Roman Lavicka·Vladimir Soucek
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Abstract

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 $\mathfrak{sl}(2,\mathbb{C}) \oplus \mathfrak{sl}(2,\mathbb{C}) = \mathfrak{so}(4,\mathbb{C})$.

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Fred Brackx, Hennie De Schepper, David Eelbode, Roman Lavicka, Vladimir Soucek. 2014-04-14. Fundaments of Quaternionic Clifford Analysis III: Fischer Decomposition in Symplectic Harmonic Analysis. https://arxiv.org/abs/1404.3625

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