The Orthogonal Branching Problem for Symplectic Monogenics

In this paper we study the sp (2m)-invariant Dirac operator D-s which acts on symplectic spinors, from an orthogonal point of view. By this we mean that we will focus on the subalgebra so(m) subset of sp (2m), as this will allow us to derive branching rules for the space of 1-homogeneous polynomial solutions for the operator D-s (hence generalising the classical Fischer decomposition in harmonic analysis for a vector variable in R-m). To arrive at this result we use techniques from representation theory, including the transvector algebra Z(sp(4), so(4)) and tensor products of Verma modules.