  Dicke states are states of a collection of particles which have been under
active investigation for several reasons. One reason is that the decay rates of
these states can be quite different from a set of independently evolving
particles. Another reason is that a particular class of these states are
decoherence-free or noiseless with respect to a set of errors. These noiseless
states, or more generally subsystems, can avoid certain types of errors in
quantum information processing devices. Here we provide a method for
calculating invariants of systems of particles undergoing collective motions.
These invariants can be used to determine a complete set of commuting
observables for a class of Dicke states as well as identify possible logical
operations for decoherence-free/noiseless subsystems. Our method is quite
general and provides results for cases where the constituent particles have
more than two internal states.
