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.
"On the ideal generated by all squarefree monomials of a given degree." J. Commut. Algebra 12 (2) 199 - 215, Summer 2020. https://doi.org/10.1216/jca.2020.12.199