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Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
| 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 | | Ideals |
| 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 link.springer.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/66647 |
| 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)
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Submitter: 寺尾 宏明
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