Disintegration of monomial representations of nilpotent Lie groups

Let G be a connected and simply connected nilpotent Lie group, let H be a closed connected subgroup of G and let chi be a unitary character of H. We construct explicitly a smooth intertwining operator between the monomial representation pi=ind(H)(G)chi of G and its decomposition into irreducibles. In particuliar, we present a new disintegration of L-2(G).