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Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements

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Title: Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
Authors: Abe, Takuro Browse this author
Terao, Hiroaki Browse this author →KAKEN DB
Keywords: Arrangement of hyperplanes
Root system
Weyl arrangement
Free arrangement
Shi arrangement
Issue Date: Feb-2016
Publisher: Springer
Journal Title: Journal of algebraic combinatorics
Volume: 43
Issue: 1
Start Page: 33
End Page: 44
Publisher DOI: 10.1007/s10801-015-0624-z
Abstract: In this article, we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual partition formula. Then, it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each subarrangement of the filtration satisfies the dual partition formula. This generalizes the main result in Abe et al. (J. Eur. Math. Soc., to appear) which affirmatively settled a conjecture by Sommers and Tymoczko (Trans. Am. Math. Soc. 358:3493-3509, 2006).
Rights: The final publication is available at
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 寺尾 宏明

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