Gauge and group properties of massless fields in any dimension

It is shown that the solvable structure of the stability group of a massless field yields, in a simple and short way, useful information about the physical polarization states, and the structure of the Hilbert space for such a field. It is also shown that such fields are necessarily gauge fields; the exact form of the gauge transformation follows from the structure of the equivalence classes implied by the group properties. Some examples for spinor and tensor fields in general dimensions are worked out and the structure of the Hilbert space for gravitational radiation is discussed in some detail.