The SO(n) invariant subspaces of polynomials of the creation operators are completely characterized by the theory of spherical harmonics, see for example, the following exposition.
Summary of the construction, Let:
$ d(z) = z_1^2+ . . . + z_n^2$
$ \Delta = (\frac{\partial}{\partial z_1})^2 + . . . + \frac{\partial}{\partial z_n})^2$
Let $\mathcal{P}_m$ be the space of homogeneous polynomials of z of degree m, and
$\mathcal{H}_m = \mathcal{P}_m \cap ker(\Delta)$
Then the SO(n) invariant subspaces are given by:
$\mathcal{P}^l_m = d^l \mathcal{H}_m $