The method of adjoint operators and a symmetry operator for the Maxwell equations in type-D vacuum backgrounds

Since in all the type-D solutions of the Einstein vacuum field equations wi th a cosmological term each maximal spin-weighted component of the electrom agnetic spinor field satisfies a decoupled equation and there exists a two- index Killing spinor field; we show, via the adjoint operators method, that a symmetry operator for the Maxwell equations can be constructed. (C) 2001 American Institute of Physics.