Symmetry operators for the conformal wave equation.

We present covariant symmetry operators for the conformal wave equation in the (off-shell) Kerr--NUT--AdS spacetimes. These operators, that are constructed from the principal Killing--Yano tensor, its `symmetry descendants', and the curvature tensor, guarantee separability of the conformal wave equation in these spacetimes. We next discuss how these operators give rise to a full set of mutually commuting operators for the conformally rescaled spacetimes and underlie the $R$-separability of the conformal wave equation therein. Then, by employing the WKB approximation to the `$\alpha$-modified conformal wave equation' we derive an associated Hamilton--Jacobi equation with a scalar curvature potential term and show its separability in the Kerr--NUT--AdS spacetimes.