dc.identifier.uri |
http://dx.doi.org/10.15488/2358 |
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dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/2384 |
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dc.contributor.author |
Abe, Takuro
|
|
dc.contributor.author |
Barakat, Mohamed
|
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dc.contributor.author |
Cuntz, Michael
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|
dc.contributor.author |
Hoge, Torsten
|
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dc.contributor.author |
Terao, Hiroaki
|
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dc.date.accessioned |
2017-11-17T12:10:54Z |
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dc.date.available |
2017-11-17T12:10:54Z |
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dc.date.issued |
2016 |
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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 |
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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 |
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dc.publisher |
Zürich : European Mathematical Society Publishing House |
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dc.relation.ispartofseries |
Journal of the European Mathematical Society 18 (2016), Nr. 6 |
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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. |
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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 |
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dc.type |
Text |
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dc.relation.issn |
1435-9855 |
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dc.relation.doi |
https://doi.org/10.4171/JEMS/615 |
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dc.bibliographicCitation.issue |
6 |
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dc.bibliographicCitation.volume |
18 |
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dc.bibliographicCitation.firstPage |
1339 |
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dc.bibliographicCitation.lastPage |
1348 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
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