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The construction of q-local superfield Lagrangian BRST quantization in non-Abelian hypergauges for generic gauge theories based on the action principle is examined in the case of reducible local superfield models (LSM) on the basis of embedding a gauge theory into a special q-local superfield model with antisymplectic constraints and a Grassmann-odd time parameter q. We examine the problem of establishing a new correspondence between the odd-Lagrangian and odd-Hamiltonian formulations of a local LSM in the case of degeneracy of the Lagrangian description with respect to derivatives over q of generalized classical superfields AI(q). We also reveal the role of the nilpotent BRST-BFV charge for a formal dynamical system corresponding to the BV-BFV dual description of an LSM.

Reducible gauge theories in local superfield Lagrangian BRST quantization