Wave and Dirac operators, and representations of the conformal group

AbstractLet M be the flat Minkowski space. The solutions of the wave equation, the Dirac equations, the Maxwell equations, or more generally the mass 0, spin s equations are invariant under a multiplier representation Us, of the conformal group. We provide the space of distributions solutions of the mass 0, spin s equations with a Hilbert space structure Hs, such that the representation Us, will act unitarily on Hs. We prove that the mass 0 equations give intertwining operators between representations of principal series. We relate these representations to the Segal-Shale-Weil (or “ladder”) representation of U(2, 2)