When are permutation invariants Cohen-Macaulay?

Fuente: arXiv
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Autores principales: Campbell, H. E. A., Wehlau, David L.
Formato: Preprint
Publicado: 2023
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author Campbell, H. E. A.
Wehlau, David L.
author_facet Campbell, H. E. A.
Wehlau, David L.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2308_09056
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle When are permutation invariants Cohen-Macaulay?
Campbell, H. E. A.
Wehlau, David L.
Commutative Algebra
13A50 (Primary) 20F55, 14M05 (Secondary)
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.
title When are permutation invariants Cohen-Macaulay?
topic Commutative Algebra
13A50 (Primary) 20F55, 14M05 (Secondary)
url https://arxiv.org/abs/2308.09056