  An explicit construction is given of a minimal free resolution of the ideal
generated by all squarefree monomials of a given degree. The construction
relies upon and exhibits the natural action of the symmetric group on the
syzygy modules. The resolution is obtained over an arbitrary coefficient ring;
in particular, it is characteristic free. Two applications are given: an
equivariant resolution of De Concini-Procesi rings indexed by hook partitions,
and a resolution of FI-modules.
