Massless particle little group ($ISO(D-2)$)

The stabilizer of a nonzero null four-momentum has connected group $ISO(D-2)$. For ordinary finite-polarization particles its translation part acts trivially, leaving a representation of $SO(D-2)$.

An ordinary massless spin-one particle has transverse vector polarizations under $SO(D-2)$. A covariant polarization satisfies $p\cdot ϵ=0$ and is identified under $ϵ\mapsto ϵ+\lambda p$. The quotient has $D-2$ positive polarizations.