On the gauge symmetries of Maxwell-like higher-spin Lagrangians

In their simplest form, metric-like Lagrangians for higher-spin massless fields display constrained gauge symmetries, unless auxiliary fields are introduced or locality is foregone. Specifically, in its standard incarnation, gauge invariance of Maxwell-like Lagrangians relies on parameters with vanishing divergence. We propose an alternative form of the corresponding local symmetry involving unconstrained parameters of mixed-symmetry type, described by rectangular two-row Young diagrams and entering high-derivative gauge transformations. The resulting gauge algebra appears to be reducible and we display the full pattern of gauge-for-gauge parameters, testing its correctness via the corresponding counting of degrees of freedom. Incidentally, this shows that massless higher spins admit a local unconstrained formulation with no need for auxiliary fields.