  Recently a new formalism for perturbations of Maxwell's equations on the
background of the Kerr-NUT-(A)dS spacetime was proposed, with which the
equations are reduced to a equation of motion of a scalar field that can be
solved by separation of variables. In this formalism the differential operators
that commute with the operators of the equations of motion, called symmetry
operators, played a key role to establish the separable structure. In this work
we propose a method to reproduce these commuting symmetry operators in terms of
the geometric quantities associated to the hidden symmetry of the background
spacetime.
