Representations of the Conformal Lie Algebra in the Space of Tensor Densities on the Sphere

Pascal Redou
2003 Journal of Nonlinear Mathematical Physics  
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 $\lambda$.
doi:10.2991/jnmp.2003.10.2.1 fatcat:zexowbxqdzgd3mgkhy3mrfcboy