BRST-BV approach for interacting higher spin fields

We develop the BRST-BV approach to construct the general off-shell Lorentz covariant cubic, quartic, $e$-tic interaction vertices for irreducible higher spin fields on $d$-dimensional Minkowski space. We consider two different cases for interacting integer higher spin fields both with massless and with massive fields. The deformation procedure to find minimal (determined with help of generalized Hilbert space) BRST-BV action for interacting higher spin fields is based on the preservation of master equation validity in each power of coupling constant $g$ starting from the Lagrangian formulation for free gauge theory. As examples we consider the construction of local cubic vertices for $k$ irreducible massless fields of integer helicities, and $k-1$ massless with one massive fields of spins $s_1, ,..., s_{k-1}, s_k$. For triple of two massless scalars and tensor field of integer spin the BRST-BV action with cubic interaction is explicitly found. Unlike the previous results on cubic vertices we follow our result for BRST approach [arXiv:2105.12030[hep-th]] for massless fields, but for the unique BRST-BV action instead of classical action with reducible gauge transformations. The procedure is based on the complete BRST operator, including the trace constraints that is used to formulate an irreducible representation with definite integer spin.