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dc.contributor.authorBuchweitz, Ragnar-Olaf
dc.contributor.authorFaber, Eleonore
dc.contributor.authorIngalls, Colin
dc.date.accessioned2018-07-04T06:52:00Z
dc.date.available2018-07-04T06:52:00Z
dc.date.issued2018-07-02
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1373
dc.description.abstractWe 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.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,14
dc.subjectReflection groupsen_US
dc.subjectHyperplane arrangementsen_US
dc.subjectMaximal Cohen–Macaulay modulesen_US
dc.subjectMatrix factorizationsen_US
dc.subjectNoncommutative desingularizationen_US
dc.titleA McKay Correspondence for Reflection Groupsen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2018-14
local.scientificprogramOWLF 2017en_US
local.series.idOWP-2018-14en_US
local.subject.msc14en_US
local.subject.msc13en_US


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