Representations of SO(3) and angular polyspectra

TL;DR

This paper characterizes the angular polyspectra of isotropic fields on the sphere using group representation theory, providing a foundation for cosmological data analysis and simulation of related coefficients.

Contribution

It introduces a novel framework based on Wigner matrices and Clebsch-Gordan coefficients for analyzing angular polyspectra of isotropic spherical fields.

Findings

Provides a basis for statistical analysis of Cosmic Microwave Background data

Outlines methods for simulating Clebsch-Gordan coefficients

Suggests applications in data compression and modeling

Abstract

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.