The theory of representations of groups SO₀(2, 1) and ISO(2, 1). Wigner coefficients of the group SO₀(2, 1)

Abstract

This paper is devoted to the representations of the groups SO(2, 1) and ISO(2, 1). Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible unitary representations of the principal continuous and supplementary as well as discrete series were obtained. Explicit expressions for spherical functions of the group SO₀(2, 1) are obtained through the Gauss hypergeometric functions. The Wigner coefficients of the group SO₀(2, 1) were computed and their explicit expressions using the bilateral series were represented. The results could be used to study the non-degenerate representations of the de Sitter group SO(3, 2).