# Spin of a gauge field

I was wondering what is the simplest way to understand the reduction of the Wigner's little group from $SO(d-1)$ to $SO(d-2)$ when one considers massive and massless fields respectively (in a $d$ dimensional spacetime). I would like a way to see this in the equations of motion. For example a spin one matter field denoted by $C_{\mu}$ can be described by $SO(d-1)$ little group. Let's now identify $C_\mu$ and $C_{\mu} +\partial_{\mu} \epsilon$ ($\epsilon$ the gauge parameter) as physically indistinguishable. How does that reduce the little group to $SO(d-2)$.