  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.
