Unfolding versus BRST and currents in Sp(2M) invariant higher-spin theory

The correspondence between BRST and unfolded formulations of field equations on group manifolds and homogeneous spaces is described. The previously introduced nonstandard BRST operator, that underlies Sp(2M) invariant higher-spin field equations, is shown to admit a natural oscillator-like realization. The coordinate independent form of conserved currents in the Sp(2M) invariant higher-spin theory is derived from the BRST formulation on Sp(2M) extended by the Heisenberg group.