  We study the general structure of correlation functions in an
Sp(2n)-invariant formulation of systems of an infinite number of higher-spin
fields. For n=4,8 and 16 these systems comprise the conformal higher-spin
fields in space-time dimensions D=4,6 and 10, respectively, while when n=2, one
deals with conventional D=3 conformal field theories of scalars and spinors. We
show that for n>2 the Sp(2n) symmetry and current conservation makes the
3-point correlators of two (rank-one or rank-two) conserved currents with a
scalar operator be that of free theory.This situation is analogous to the one
in conventional conformal field theories, where conservation of higher-spin
currents implies that the theories are free.
