We study necessary and sufficient conditions for the existence of mocklets, the admissible vectors of a class of unitary non irreducible representations of certain semi-direct products. This class of representations generalizes the restriction of the metaplectic representation to triangular subgroups of the symplectic group. Our theory includes many known examples in signal analysis, especially wavelets and shearlets. We focus on an example where translations are replaced by the group associated with a second order differential operator. This is a joint work with Ernesto De Vito.