Decomposition of the principal series of unitary irreducible representations of SU(2,2) restricted to the subgroup SU(1,1) x SU(2)

An explicit form is given for the unitary irreducible representations of the principal nondegenerate series of the group SU(2, 2). These representations are then restricted to the subgroup SU(1,1)⊗SU(2) and are found to be equivalent to the regular representation of SU(1,1)⊗SU(2).