Wigner Coefficients for the Group E(2)

Abstract

The Wigner coefficients for the faithful unitary representations of the 2-dimensional Euclidean group are derived from two identities involving Bessel functions. Since the multiplicity in the decomposition of a direct product is two, we find two sets of coefficients which are real and mutually orthogonal and symmetric and antisymmetric, respectively, under interchange of constituent representations. Properties of the coefficients at the ends of the decomposition spectrum are discussed.