Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424402 | European Journal of Combinatorics | 2011 | 8 Pages |
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 HâA 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 HâA 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Takuro Abe, Hiroaki Terao,