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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The authors kindly acknowledge financial support by the E. Cech Institute, more particularly from grant P201/12/G028 of the Grant Agency of the Czech Republic.
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Brackx, F., De Schepper, H., Eelbode, D. et al. Fischer decomposition in symplectic harmonic analysis. Ann Glob Anal Geom 46, 409–430 (2014). https://doi.org/10.1007/s10455-014-9431-3
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DOI: https://doi.org/10.1007/s10455-014-9431-3