Representations of the conformal Lie algebra in the space of tensor densities on the sphere

Abstract

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$unitarysubmodulesof${\mathcal F}_λ(\mathbb{S}^n)$asafunctionof$λ$.

arXiv commentPublished by JNMP at http://www.sm.luth.se/math/JNMP/