For SU(2) rotational invariance there is a clear interpretation of what all the generators mean. They correspond to operators whose eigenvalues are some observable. The noether charges correspond to the x,y and z components of angular momentum. The casimir is just the total angular momentum squared. I want a similar interpretation for SU(2) weak and SU(3) colour in the standard model. For SU(2) weak there is one casimir and 3 generators - What observable quantities do they correspond to? SU(3) has 2 casimirs and 8 generators, again what observables do these correspond to?