  We study a dual pair of general linear Lie superalgebras in the sense of R.
Howe. We give an explicit multiplicity-free decomposition of a symmetric and
skew-symmetric algebra (in the super sense) under the action of the dual pair
and present explicit formulas for the highest weight vectors in each isotypic
subspace of the symmetric algebra. We give an explicit multiplicity-free
decomposition into irreducible $gl(m|n)$-modules of the symmetric and
skew-symmetric algebras of the symmetric square of the natural representation
of $gl(m|n)$. In the former case we find as well explicit formulas for the
highest weight vectors. Our work unifies and generalizes the classical results
in symmetric and skew-symmetric models and admits several applications.
