UNITARY REPRESENTATIONS OF POINCARE GROUP CONTAINED IN A CLASS OF REPRESENTATIONS OF CONFORMAL GROUP

A unitary irreducible class of representations of the conformal group is constructed and reduced with respect to the Poincaré group to see which unitary irreducible representations of the Poincaré group it contains. In particular, it is shown that this class of representations of the conformal group does not contain the continuous-spin representations of the Poincaré group. It is concluded that the representations of the conformal group cannot be used to eliminate the continuous-spin representations.