Quartet unconstrained formulation for massless higher spin fields

We construct simple unconstrained Lagrangian formulations for massless higher spin fields in flat space of arbitrary dimension and on anti-de Sitter background. Starting from the triplet equations of Francia and Sagnotti, which describe a chain of spin modes, we introduce an auxiliary field and find appropriate gauge invariant constraints that single out the spin-s mode. The resulting quartet of fields, thus describing an irreducible representation of the Poincaré group, is used to construct simple Lagrangian formulations, which are local, free from higher derivative terms and use equal number of auxiliary fields for an unconstrained description of any value of spin. Our method proves to be most efficient for an unconstrained description of massless higher spin fermions in anti-de Sitter space. A relation of the minimal models with the universal BRST approach is discussed.