Representations of SO(3) and angular polyspectra

Details Representations of SO(3) and angular polyspectra Representations of SO(3) and angular polyspectra

2008-07-04

arxiv.org/abs/0807.0687v1

Journal of Multivariate Analysis, Vol. 101 (2010), pp.77-100

Mathematics

Probability

29 pages

Scientific paper

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2. Our techniques rely heavily on group representation theory, and specifically on the properties of Wigner matrices and Clebsch-Gordan coefficients. The findings of the present paper constitute a basis upon which one can build formal procedures for the statistical analysis and the probabilistic modelization of the Cosmic Microwave Background radiation, which is currently a crucial topic of investigation in cosmology. We also outline an application to random data compression and "simulation" of Clebsch-Gordan coefficients.

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