Buchweitz, R-O, Faber, E orcid.org/0000-0003-2541-8916 and Ingalls, C (2020) A McKay correspondence for reflection groups. Duke Mathematical Journal, 169 (4). pp. 599-669. ISSN 0012-7094
Abstract
We construct a noncommutative desingularization of the discriminant of a finite reflection group G as a quotient of the skew group ring A=S∗G. If G is generated by order 2 reflections, then this quotient identifies with the endomorphism ring of the reflection arrangement A(G) viewed as a module over the coordinate ring SG/(Δ) of the discriminant of G. This yields, in particular, a correspondence between the nontrivial irreducible representations of G to certain maximal Cohen–Macaulay modules over the coordinate ring SG/(Δ). These maximal Cohen–Macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement A(G) viewed as a module over SG/(Δ). We identify some of the corresponding matrix factorizations, namely, the so-called logarithmic (co-)residues of the discriminant.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020. This is an author produced version of an article published in Duke Mathematical Journal. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | reflection groups; hyperplane arrangements; maximal Cohen–Macaulay modules; matrix factorizations; noncommutative desingularization |
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) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Jun 2020 14:20 |
Last Modified: | 24 Jun 2020 15:10 |
Status: | Published |
Publisher: | Duke University Press |
Identification Number: | 10.1215/00127094-2019-0069 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162264 |