A Note on S.Weinberg, "Massless Particles in Higher Dimensions"

In [1], Weinberg made a conjecture about the little-group representations of massless particles that can be created out of the vacuum by the action of a local operator in $d$ dimensions, generalizing his old result [2] in $d=4$. In this note, I prove his conjecture and extend it to arbitrary irreps of $so(1,d-1)$.