Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields

Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[{\widehat{s}}_1,{\widehat{s}}_2]$ with two columns are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a BRST approach extending the results of [arXiv:1412.0200[hep-th]]. A Lorentz-invariant resolution of the BRST complex within both the constrained and unconstrained BRST formulations produces a gauge-invariant Lagrangian entirely in terms of the initial tensor field $\Phi_{[\mu]_{\hat{s}1}, [\mu]{\hat{s}_2}}$subjectto$Y[\hat{s}_1,\hat{s}_2]$ with an additional tower of gauge parameters realizing the $({\widehat{s}}_1-1)$-th stage of reducibility with a specific dependence on the value $({\widehat{s}}_1-{\widehat{s}}_2)=0,1,\mathrm{.}\mathrm{.}\mathrm{.},{\widehat{s}}_1$. Minimal BRST–BV action is suggested, being proper solution to the master equation in the minimal sector and providing objects appropriate to construct interacting Lagrangian formulations with mixed-antisymmetric fields in a general framework.