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

摘要

Using a technique of Kalnins, unitary irreducible rep-resentation ( UIR) of principle series of SO(2; 1), decomposed ac-cording to the group T1, are realized in the space of homogeneousfunctions on the cone?20 ? ?21 ? ?22 = 0as the carrier space. It is then shown that the matrix element of anarbitrary ˉnite rotation of SO(2; 1) are determined by those of twospeciˉc types of ˉnite rotations, each depending on a single para-meter; matrix elements of these two speciˉc types of ˉnite rotationsare then explicitly computed. Finally, a number of new relationsbetween special functions appearing in these matrix elements, areobtained by using the usual standard techniques of deriving suchrelations with the help of group representation theory.