The freeness of ideal subarrangements of Weyl arrangements

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dc.identifier.uri Abe, Takuro Barakat, Mohamed Cuntz, Michael Hoge, Torsten Terao, Hiroaki 2017-11-17T12:10:54Z 2017-11-17T12:10:54Z 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:
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.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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