Fundaments of Quaternionic Clifford Analysis III: Fischer Decomposition in Symplectic Harmonic Analysis
Brackx, Fred · De Schepper, Hennie · Eelbode, David · Lavicka, Roman · Soucek, Vladimir
Original · EN
In the framework of quaternionic Clifford analysis in Euclidean space R⁴ᵖ, 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 sl(2,C) ⊕ sl(2,C) = so(4,C).
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