The theory of representations of groups $SO_{0}(2,1)$ and $ISO(2,1)$. Wigner coefficients of the group $SO_{0}(2,1)$

Bala Ali Rajabov

paper

The theory of representations of groups $S O_{0} (2, 1)$ and $I S O (2, 1)$ . Wigner coefficients of the group $S O_{0} (2, 1)$

arXiv:1710.10425

Abstract

This paper is devoted to the representations of the groups $S O (2, 1)$ and $I S O (2, 1)$ . 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 $S O_{0} (2, 1)$ are obtained through the Gauss hypergeometric functions. The Wigner coefficients of the group $S O_{0} (2, 1)$ 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 $S O (3, 2)$ .

12 pages

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

Abstract

The theory of representations of groups $S O_{0} (2, 1)$ and $I S O (2, 1)$ . Wigner coefficients of the group $S O_{0} (2, 1)$