ar X iv : 0 80 7 . 06 87 v 1 [ m at h . PR ] 4 J ul 2 00 8 Representations of SO ( 3 ) and angular polyspectra
نویسندگان
چکیده
We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S 2 = ˘ (x, y, z) : x 2 + y 2 + z 2 = 1 ¯. 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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