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A recent progress in a gauge-invariant Lagrangian description of massive andmassless half-integer higher-spin fields in AdS and Minkowski spaces ispresented. The procedure is based on a BFV-BRST operator, encoding the initialconditions realized by constraints in a Fock space and extracting thehigher-spin fields from unitary irreducible representations of the AdS(Poincare) group. The construction is applicable to higher-spin tensor fieldswith a multi-row Young tableaux.

On Lagrangian Formulation for Half-integer HS Fields within Hamiltonian BRST Approach