  The Robertson-Walker spacetimes are conformally flat and so are conformally
invariant under the action of the Lie group SO(4,2), the conformal group of
Minkowski spacetime. We find a local coordinate transformation allowing the
Robertson-Walker metric to be written in a manifestly conformally flat form for
all values of the curvature parameter k continuously and use this to obtain the
conformal Killing vectors of the Robertson-Walker spacetimes directly from
those of the Minkowski spacetime. The map between the Minkowski and
Robertson-Walker spacetimes preserves the structure of the Lie algebra so(4,2).
Thus the conformal Killing vector basis obtained does not depend upon k, but
has the disadvantage that it does not contain explicitly a basis for the
Killing vector subalgebra. We present an alternative set of bases that depend
(continuously) on k and contain the Killing vector basis as a sub-basis (these
are compared with a previously published basis). In particular, bases are
presented which include the Killing vectors for all Robertson-Walker spacetimes
with additional symmetry, including the Einstein static spacetimes and the de
Sitter family of spacetimes, where the basis depends on the Ricci scalar R.
