The freeness of ideal subarrangements of Weyl arrangements

 dc.identifier.uri http://dx.doi.org/10.15488/2358 dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2384 dc.contributor.author Abe, Takuro dc.contributor.author Barakat, Mohamed dc.contributor.author Cuntz, Michael dc.contributor.author Hoge, Torsten dc.contributor.author Terao, Hiroaki dc.date.accessioned 2017-11-17T12:10:54Z dc.date.available 2017-11-17T12:10:54Z dc.date.issued 2016 dc.identifier.citation Abe, T.; Barakat, M.; Cuntz, M.; Hoge, T.; Terao, H.: The freeness of ideal subarrangements of Weyl arrangements. In: Journal of the European Mathematical Society 18 (2016), Nr. 6, S. 1339-1348. DOI: https://doi.org/10.4171/JEMS/615 dc.description.abstract A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers-Tymoczko. In particular, when an ideal subarrangement is equal to the entire Weyl arrangement, our main theorem yields the celebrated formula by Shapiro, Steinberg, Kostant, and Macdonald. The proof of the main theorem is classification-free. It heavily depends on the theory of free arrangements and thus greatly differs from the earlier proofs of the formula. © European Mathematical Society 2016. eng dc.language.iso eng dc.publisher Zürich : European Mathematical Society Publishing House dc.relation.ispartofseries Journal of the European Mathematical Society 18 (2016), Nr. 6 dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. dc.subject Arrangement of hyperplanes eng dc.subject Dual partition theorem eng dc.subject Free arrangement eng dc.subject Ideals eng dc.subject Root system eng dc.subject Weyl arrangement eng dc.subject.ddc 510 | Mathematik ger dc.title The freeness of ideal subarrangements of Weyl arrangements eng dc.type article dc.type Text dc.relation.issn 1435-9855 dc.relation.doi https://doi.org/10.4171/JEMS/615 dc.bibliographicCitation.issue 6 dc.bibliographicCitation.volume 18 dc.bibliographicCitation.firstPage 1339 dc.bibliographicCitation.lastPage 1348 dc.description.version publishedVersion tib.accessRights frei zug�nglich
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