Affiliation:
1. Departement of Matematics Universiteit Antwerpen Antwerp Belgium
Abstract
In this paper, we develop the Hermitian refinement of symplectic Clifford analysis, by introducing a complex structure
on the canonical symplectic manifold
. This gives rise to two symplectic Dirac operators
and
(in the sense of Habermann), leading to a
‐invariant system of equations on
. We discuss the solution space for this system, culminating in a Fischer decomposition for the space of (harmonic) polynomials on
with values in the symplectic spinors. To make this decomposition explicit, we will construct the associated embedding factors using a transvector algebra.
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