  We compute the motions of null infinity to which the components of the
angular momentum of the gravitational field, as defined by Penrose, are
conjugate. We find that the boosts are supplemented by anomalous translations.
If $c_{ab}$ is the skew bivector determining the component of the angular
momentum in question, the anomaly is proportional to $$c_{ab}t^b\phi ^{ad}\,
,$$ where $t^a$ is a unit vector in the direction of the Bondi--Sachs momentum
and $\phi _{ab}$ is the quadrupole moment of the shear of the cut at which the
angular momentum is evaluated. This effect persists in the weak--field limit.
This surprising result is a general consequence of the requirement that angular
momentum be supertranslation--invariant in a quiescent regime, and not some
essentially twistorial peculiarity.
