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

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

2003-10-24

arxiv.org/abs/math/0310392v1

J. Nonlinear Math. Phys., volume 10, no. 2 (2003) 136-140

Mathematics

Differential Geometry

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

Scientific paper

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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