  Let ${\mathcal F}_\lambda(\mathbb{S}^n)$ be the space of tensor densities on
$\mathbb{S}^n$ of degree $\lambda$. We consider this space as an induced module
of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and
classify $(\mathrm{so}(n+1,1),\mathrm{SO}(n+1))$-sim$unitary submodules of
${\mathcal F}_\lambda(\mathbb{S}^n)$ as a function of $\lambda$.
