The orthogonal branching problem for symplectic monogenics

Abstract

In this paper we study the sp(2m)-invariant Dirac operator Ds which acts on symplectic spinors, from an orthogonal point of view. By this we mean that we will focus on the subalgebra so(m) ⊂ sp(2m), as this will allow us to derive branching rules for the space of 1-homogeneous polynomial solutions for the operator Ds (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.