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arXiv · 2308.09056

When are permutation invariants Cohen-Macaulay?

H. E. A. Campbell·David L. Wehlau
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Abstract

Over a field of characteristic 0, every ring of invariants of a finite group is Cohen-Macaulay. This is not true for fields of positive characteristic. We consider permutation representations and their invariant rings over fields $\mathbb{F}_p$ of prime order. We give an efficient algorithm which for any given permutation representation, determines those primes $p$ for which the invariant ring over $\mathbb{F}_p$ is Cohen-Macaulay, using linear algebra over $\ZZ$. A generalization of the classical discriminant associated to the alternating group is defined for subgroups of certain finite unitary complex reflection groups.

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H. E. A. Campbell, David L. Wehlau. 2023-08-17. When are permutation invariants Cohen-Macaulay?. https://arxiv.org/abs/2308.09056

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