dc.contributor.author Buchweitz, Ragnar-Olaf dc.contributor.author Faber, Eleonore dc.contributor.author Ingalls, Colin dc.date.accessioned 2018-07-04T06:52:00Z dc.date.available 2018-07-04T06:52:00Z dc.date.issued 2018-07-02 dc.identifier.uri http://publications.mfo.de/handle/mfo/1373 dc.description.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 two reflections, then this quotient identifies with the endomorphism ring of the reflection arrangement $\mathcal{A}(G)$ viewed as a module over the coordinate ring $S^G/(\Delta)$ 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 $S^G/(\Delta)$. These maximal Cohen--Macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement $\mathcal{A} (G)$ viewed as a module over $S^G/(\Delta)$. We identify some of the corresponding matrix factorizations, namely the so-called logarithmic co-residues of the discriminant. en_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,14 dc.subject Reflection groups en_US dc.subject Hyperplane arrangements en_US dc.subject Maximal Cohen–Macaulay modules en_US dc.subject Matrix factorizations en_US dc.subject Noncommutative desingularization en_US dc.title A McKay Correspondence for Reflection Groups en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-14 local.scientificprogram OWLF 2017 en_US local.series.id OWP-2018-14 en_US local.subject.msc 14 en_US local.subject.msc 13 en_US
﻿