A Hermitian refinement of symplectic Clifford analysis

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.