Fischer decomposition in symplectic harmonic analysis

Abstract

In the framework of quaternionic Clifford analysis in Euclidean space, 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 also determined.

Keywords

• Quaternionic Clifford analysis
• Symplectic harmonics
• Fischer decomposition