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The key aspects of a gauge-invariant Lagrangian description of massive andmassless half-integer higher-spin fields in AdS spaces with a two-row Youngtableaux $Y(s_1,s_2)$ are presented in an unconstrained description, as well asin off-shell formulations with algebraic constraints, on the basis of BFV-BRSToperators for non-linear operator superalgebras, encoding the initialconditions realized by constraints in a Fock space and extracting thehigher-spin fields from unitary representations of the AdS group.

On Lagrangian formulations for mixed-symmetry HS fields on AdS spaces within BFV-BRST approach