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

被引：10

作者：

Abe, Takuro ^{[1
]}

Terao, Hiroaki ^{[2
]}

机构：

[1] Kyoto Univ, Dept Mech Engn & Sci, Kyoto 6068501, Japan

[2] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2016年 / 43卷 / 01期

关键词：

Arrangement of hyperplanes; Root system; Weyl arrangement; Free arrangement; Shi arrangement; Ideals;

D O I：

10.1007/s10801-015-0624-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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).

引用

页码：33 / 44

页数：12

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