Decomposition of the Unitary Irreducible Representations of the Group <i>SL</i>(2<i>C</i>) Restricted to the Subgroup <i>SU</i>(1, 1)

Abstract

The unitary irreducible representations of the group SL(2C) belonging to the principal series restricted to the subgroup SU(1, 1) are decomposed into a direct integral of unitary irreducible representations of SU(1, 1). The matrix elements of the unitary operator which performs the decomposition are given explicitly and used to obtain a relation between the matrix elements of the unitary irreducible representations of the groups SL(2C) and SU(1, 1). Similar identities between the matrix elements of nonunitary representations of these groups are obtained by means of analytic continuation. The relevance of these results to the theory of complex angular momentum and of high energy nearly forwardscattering is pointed out.