Frame-like off-shell dualization for mixed-symmetry gauge fields

We construct a purely frame-like parent action that allows us to dualize, at the off-shell level, an arbitrary mixed-symmetry bosonic massless field in Minkowski background of dimensions d. Starting from any massless mixed-symmetry gauge field in the standard Skvortsov frame-like formulation and following an off-shell dualization procedure, we obtain dual theories which are on-shell related by so(d - 2) Hodge duality. The Hodge dualization can be done on any column of the Young diagram characterizing the generalized spin of the original frame-like field. Dualization with respect to the first column of the Young diagram leads to a standard frame-like action for the dual field. Any other dualization results in an action which cannot be described by the standard frame-like formalism, as the on-shell field is not so(d - 2) traceless. Instead, the latter field is given by the product of an irreducible traceless tensor and a certain number of so(d - 2)-invariant metrics, and the corresponding dual frame-like action is new. Such actions require supplementary fields, which naturally arise along the lines of the approach that we propose.