  BRST-BFV method for constrained Lagrangian formulations (LFs) for
(ir)reducible half-integer HS Poincare group representations in Minkowski space
is suggested. The procedure is derived by 2 ways: from the unconstrained
BRST-BFV method for mixed-symmetry HS fermionic fields subject to an arbitrary
Young tableaux with k rows (suggested in arXiv:1211.1273[hep-th]) by extracting
the second-class constraints, $\widehat{O}_\alpha=(\widehat{O}_a,
\widehat{O}^+_a)$, from a total superalgebra of constraints, second, in
self-consistent way by means of finding BRST-extended initial off-shell
algebraic constraints, $\widehat{O}_a$. In both cases, the latter constraints
supercommute on the constraint surface with constrained BRST $Q_C$ and spin
operators $\sigma^i_C$. The closedness of the superalgebra $Q_C, \widehat{O}_a,
\sigma^i_C$ guarantees that the final gauge-invariant LF is compatible with
off-shell constraints $\widehat{O}_a$ imposed on field and gauge parameter
vectors of Hilbert space not depending from the ghosts and conversion auxiliary
oscillators related to $\widehat{O}_a$, in comparison with vectors for
unconstrained BRST-BFV LF. The suggested constrained BRST-BFV approach is valid
for both massive HS fields and integer HS fields in the second-order
formulation. It is shown that the respective constrained and unconstrained LFs
for (half)-integer HS fields with a given spin are equivalent. The constrained
Lagrangians in ghost-independent and component (for initial spin-tensor field)
are obtained and shown to coincide with Fang-Fronsdal formulation for
constrained totally-symmetric HS field. The triplet and unconstrained quartet
LFs for the latter field and gauge-invariant constrained Lagrangians for a
massive field of spin n+1/2 are derived. A concept of BRST-invariant
second-class constraints for a general dynamical system with mixed-class
constraints is suggested.
