On the Dynin-Folland Group and its Applications to Modulation Spaces on Coadjoint Orbits

We give a classification of the unitary irreducible representations (unirreps) of the Dynin-Folland Group, a.k.a. the Heisenberg Group of the Heisenberg Group, and discuss the modulation spaces induced by these unirreps on their corresponding co-adjoint orbits via the Weyl-Pedersen calculus. We compare these spaces with both the classical modulation spaces and the co-orbit modulation spaces induced by the Dynin-Folland group.