  In this note we show that the complete symmetric polynomials are dual
generators of compressed artinian Gorenstein algebras satisfying the Strong
Lefschetz Property. This is the first example of an explicit dual form with
these properties.
  For complete symmetric forms of any degree in any number of variables, we
provide an upper bound for the Waring rank by establishing an explicit power
sum decomposition.
  Moreover, we determine the Waring rank, the cactus rank, the resolution and
the Strong Lefschetz Property for any Gorenstein algebra defined by a symmetric
cubic form. In particular, we show that the difference between the Waring rank
and the cactus rank of a symmetric cubic form can be made arbitrarily large by
increasing the number of variables.
  We provide upper bounds for the Waring rank of generic symmetric forms of
degrees four and five.
