Unitary representations of the (4 + 1) de Sitter group on unitary irreducible representation spaces of the Poincaré group: Equivalence with their realizations as induced representations

In a previous work we have constructed realizations of the principal continuous series of unitary irreducible representations of the simply connected covering group of the (4 + 1) de Sitter group on unitary irreducible representation spaces of the simply connected covering group of the Poincaré group. In this work we demonstrate the equivalence of the representations constructed in the previous work with their realizations as induced representations.