We develop the BRST approach to gauge invariant Lagrangian construction for the massive mixed symmetry integer higher spin fields described by the rank-two Young tableaux in arbitrary dimensional Minkowski space. The theory is formulated in terms of auxiliary Fock space. No off-shell constraints on the fields and the gauge parameters are imposed. The approach under consideration automatically leads to a gauge invariant Lagrangian for massive theory with all appropriate Stuckelberg fields. It is shown that all the restrictions defining an irreducible representation of the Poincare group arise from Lagrangian formulation as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive the gauge-invariant Lagrangian for massive rank-2 antisymmetric tensor field containing the complete set of auxiliary fields and gauge parameters.
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