The freeness of Shi-Catalan arrangements

Takuro Abe, Hiroaki Terao

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1191-1198
Number of pages8
JournalEuropean Journal of Combinatorics
Volume32
Issue number8
DOIs
Publication statusPublished - Nov 1 2011
Externally publishedYes

Fingerprint

Hyperplane
Arrangement
Equivariant
Weyl Group
Perpendicular
Finite Group
Orbit
Roots
Generalise
Integer
Theorem

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

The freeness of Shi-Catalan arrangements. / Abe, Takuro; Terao, Hiroaki.

In: European Journal of Combinatorics, Vol. 32, No. 8, 01.11.2011, p. 1191-1198.

Research output: Contribution to journalArticle

Abe, Takuro ; Terao, Hiroaki. / The freeness of Shi-Catalan arrangements. In: European Journal of Combinatorics. 2011 ; Vol. 32, No. 8. pp. 1191-1198.
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