Representations of SO(3) and angular polyspectra

We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S2 = (x, y, z) : x2 + y2 + z2 = 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. Key Words. Group Representations; Isotropy; Polyspectra; Spherical Random Fields. AMS 2000 Classification. 60G10; 60G35; 20C12; 20C35

• Type: Journal
• Year: 2010
• Where: MA
• Authors: D. Marinucci, G. Peccati
• Keywords: Clebsch-Gordan Coefficients, Communications, Cosmic Microwave Background Radiation, Group Representations, MA 2010