Unitary Irreducible Representation ( UIR) Matrix Elements of Finite Rotations of SO(2, 1) Decomposed According to the Subgroup T1

Abstract

Using a technique of Kalnins, unitary irreducible representation ( UIR) of principle series of SO(2, 1), decomposed according to the group T1, are realized in the space of homogeneous functions on the cone ξ20 − ξ21 − ξ22 = 0as the carrier space. It is then shown that the matrix element of an arbitrary finite rotation of SO(2, 1) are determined by those of two specific types of finite rotations, each depending on a single parameter; matrix elements of these two specific types of finite rotations are then explicitly computed. Finally, a number of new relations between special functions appearing in these matrix elements, are obtained by using the usual standard techniques of deriving such relations with the help of group representation theory.