Abstract
We extend the results of Lagrangian formulations study to construct gauge-invariant Lagrangians for (ir)reducible integer higher-spin massless and massive representations of the Poincaré group with a Young tableau \(Y[\hat{s}_{1},\hat{s}_{2},\hat{s}_{3}]\) in \(d\) -dimensional flat space-time (as the probable candidates to describe the dark matter problem beyond the SM). These particles are described within a metric-like formulation by tensor fields with 3 groups of antisymmetric Lorentz indices \(\Phi_{\mu^{1}[{\hat{s}_{1}}],\mu^{2}[{\hat{s}_{2}}],\mu^{3}[{\hat{s}_{3}}]}\) on a basis of the BRST method with complete, \(Q\) , and incomplete, \(Q_{c}\) , BRST operators. We found unconstrained (with \(Q\) ) and constrained (with \(Q_{c}\) and off-shell BRST invariant holonomic constraints) gauge Lagrangian formulations with different configuration spaces and reducibility stages. The deformation procedure to construct interacting gauge model with mixed-antisymmetric fields is proposed.
