arXiv subjects
Publications and source records attributed to Pascal Redou.
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 $\lambda$.
We consider the space of tensor densities on the n-dimensional sphere with degree lambda (or, equivalently, of conformal densities with degree lambda). This space is a module over the group of diffeomorphisms, and consequently over the Lie algebra of vector fields, on the sphere, and we first prove that as a module over the conformal group, it is infinitesimally equivalent to an induced module from the principal series, precisely from the nonunitary spherical series on the space of smooth functions on the sphere. In function of lambda,(g,K)-simple and unitary submodules of the space of tensor densities are therefore classified.