Quantification of a massive orbit of a generalized Poincare group

Let G be the generalized Poincare group Rn+1 x SO0 (n, 1) and O be a coadjoint orbit of G with little group SO(n). We give a symplectomorphism from R-2n x O to O, where O' is a coadjoint orbit of SO(n). When O is entire and associated to a unitary irreducible representation (n) over bar of G, we construct a Weyl correspondence on O adapted to pi.