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

Pascal Redou

doi:10.2991/jnmp.2003.10.2.1

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

Pascal Redou

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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$unitary submodules of ${\mathcal F}_\lambda(\mathbb{S}^n)$ as a function of $\lambda$.

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Pascal Redou. 2003-10-24. Representations of the conformal Lie algebra in the space of tensor densities on the sphere. https://doi.org/10.2991/jnmp.2003.10.2.1

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