On First Order Symmetry Operators for the Field Equations of Differential Forms

We consider first order symmetry operators for the equations of motion of differential $p$-form fields in general $D$-dimensional background geometry of any signature for both massless and massive cases. For $p=1$ and $p=2$ we give the general forms of the symmetry operators. Then we find a class of symmetry operators for arbitrary $p$ and $D$, which is naturally suggested by the lower $p$ results.