The freeness of Shi-Catalan arrangements

Takuro Abe, Hiroaki Terao

研究成果: Contribution to journalArticle査読

5 被引用数 (Scopus)

抄録

Let W be a finite Weyl group and A be the corresponding Weyl arrangement. A deformation of A is an affine arrangement which is obtained by adding to each hyperplane H∈A several parallel translations of H by the positive root (and its integer multiples) perpendicular to H. We say that a deformation is W-equivariant if the number of parallel hyperplanes of each hyperplane H∈A depends only on the W-orbit of H. We prove that the conings of the W-equivariant deformations are free arrangements under a Shi-Catalan condition and give a formula for the number of chambers. This generalizes Yoshinaga's theorem conjectured by Edelman-Reiner.

本文言語英語
ページ(範囲)1191-1198
ページ数8
ジャーナルEuropean Journal of Combinatorics
32
8
DOI
出版ステータス出版済み - 11 2011
外部発表はい

All Science Journal Classification (ASJC) codes

  • 離散数学と組合せ数学

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