Reduction of irreducible unitary representations of generalized Poincaré groups with respect to their subgroups

We consider the problem of the reduction of unitary irreducible representations of the generalized Poincaré groups $\mathscr P(1,n)$ with respect to their subgroups $\mathscr P(1, n-k)$. We find the explicit form of the unitary operator that relates the canonical basis of the representation to the $\mathscr P(1, n-k)$-basis. The action of the generators in the $\mathscr P(1, n-k)$-basis is given explicitly. The case of the inhomogeneous de Sitter group is considered in detail.