On the ideal generated by all squarefree monomials of a given degree
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2016
- DOI:
- 10.48550/arXiv.1609.06396
- arXiv:
- arXiv:1609.06396
- Bibcode:
- 2016arXiv160906396G
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Representation Theory;
- 13D02;
- 13A50
- E-Print:
- Updated references