Faber, E. orcid.org/0000-0003-2541-8916, Ingalls, C., May, S. et al. (1 more author) (Cover date: November–December 2024) Matrix factorizations of the discriminant of Sn. Journal of Symbolic Computation. 102310. ISSN 0747-7171
Abstract
Consider the symmetric group Sn acting as a reflection group on the polynomial ring k[x₁..., xn)] where k is a field, such that Char(k) does not divide n!. We use Higher Specht polynomials to construct matrix factorizations of the discriminant of this group action: these matrix factorizations are indexed by partitions of n and respect the decomposition of the coinvariant algebra into isotypical components. The maximal Cohen–Macaulay modules associated to these matrix factorizations give rise to a noncommutative resolution of the discriminant and they correspond to the nontrivial irreducible representations of Sn). All our constructions are implemented in Macaulay2 and we provide several examples. We also discuss extensions of these results to Young subgroups of Sn) and indicate how to generalize them to the reflection groups G (m, 1,n).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/). |
Keywords: | Matrix factorizations, Discriminants of reflection groups, Higher Specht polynomials, Maximal Cohen–Macaulay modules |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/W007509/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 Feb 2024 11:28 |
Last Modified: | 29 Feb 2024 11:38 |
Published Version: | https://www.sciencedirect.com/science/article/pii/... |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jsc.2024.102310 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:209753 |
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