  We consider first order linear operators commuting with the operator
appearing in the linearized equation of motion of Rarita-Schwinger fields which
comes directly from the action. First we consider a simplified operator giving
an equation equivalent to the original equation, and classify first order
operators commuting with it in four dimensions. In general such operators are
symmetry operators of the original operator, but we find that some of them
commute with it. We extend this result in four dimensions to arbitrary
dimensions and give first order commuting operators constructed of odd rank
Killing-Yano and even rank closed conformal Killing-Yano tensors with
additional conditions.
