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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
ξ
2
0 − ξ
2
1 − ξ
2
2 = 0
as 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.
Ansaruddin Syed. (2016) Unitary Irreducible Representation ( UIR) Matrix Elements of Finite Rotations of SO(2, 1) Decomposed According to the Subgroup T1, , Volume 48, Issue 1.
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