  We introduce the class of principal symmetric ideals, which are ideals
generated by the orbit of a single polynomial under the action of the symmetric
group. Fixing the degree of the generating polynomial, this class of ideals is
parametrized by points in a suitable projective space. We show that the minimal
free resolution of a principal symmetric ideal is constant on a nonempty
Zariski open subset of this projective space and we determine this resolution
explicitly. Along the way, we study two classes of graded algebras which we
term narrow and extremely narrow; both of which are instances of compressed
artinian algebras.
