On covariant cubic vertices for irreducible HS fields with integer and half-integer spins on flat backgrounds

Higher-spin fields (for s≥2) are included into the spectrum of superstring theory, which describes gravitational interaction at an early stage of the Universe evolution and seem to be by natural candidates for describing Dark Matter. The note proposes a procedure for constructing Poincare-covariant Lagrangian cubic interaction vertices (previously known only in the light-cone formalism) for massless irreducible fields of higher integer and half-integer spins on Minkowski space-time of arbitrary dimension within the Becchi-Rouet-Stora-Tyutin (BRST) approach with an incomplete BRST operator. The consideration is based on the second order Lagrangian formulations for free totally-symmetric irreducible tensor and spin-tensor fields with Abelian gauge symmetries, which are deformed with the preservation of the number of physical degrees of freedom to a cubically interacting theory with non-Abelian gauge algebra. General cubic interaction for the fields with helicities n1+1/2, n2+1/2, s3, as in the Standard Model, contains two types of vertices to be BRST closed solutions of the generating equations, satisfying as well to gamma-traceless? traceless constraints and to the spin conditions.