Towards Lagrangian Dynamics for Constrained Mixed-Symmetric Interacting Higher-Spin Fields

The necessary and sufficient conditions to construct consistent Lagrangian formulation for irreducible interacting massless higher-spin (HS) fields on d-dimensional Minkowski space within approach with incomplete BRST operator and off-shell holonomic constraints are found. It is shown that in addition to superconmmuting of incomplete BRST operator with appropriate traceless and Young constraints, which annihilate the field and gauge parameter vectors, these constraints should form Abelian superalgebra both with BRST operator and with operators of cubic, quartic and etc. vertices. The consistent deformation of free model with constrained HS fields with integer spin requires for the cubic vertex to be by BRST-closed, traceless and Young-symmetric solution of the generating equations. The explicit form for the vertices for irreducible constrained interacting fields are obtained by means of projectors on traceless and Young-symmetric modes.