In this paper, we will prove that the reproducing kernels \(Z_k({\underline{x}},{\underline{u}})\) for the spaces \({\mathcal {H}}_k({\mathbb {R}}^m,{\mathbb {C}})\) of k-homogeneous harmonics can be seen as elements of an infinite-dimensional ladder operator representation for a cubic polynomial angular momentum algebra which is known as the Higgs algebra. This algebra will be shown to be one of two direct summands in a transvector algebra which is related to the harmonic Fischer decomposition in two vector variables.
