English

Tilings defined by affine Weyl groups

Group Theory 2011-10-10 v2

Abstract

Let W be a Weyl group, presented as a crystallographic reflection group on a Euclidean vector space V, and C an open Weyl chamber. In a recent paper, Waldspurger proved that the images (id-w)(C), for Weyl group elements w, are all disjoint, and their union is the closed cone spanned by the positive roots. We show that similarly, if A is the Weyl alcove, the images (id-w)(A), for affine Weyl group elements w, are all disjoint, and their union is V.

Keywords

Cite

@article{arxiv.0811.3880,
  title  = {Tilings defined by affine Weyl groups},
  author = {Eckhard Meinrenken},
  journal= {arXiv preprint arXiv:0811.3880},
  year   = {2011}
}

Comments

9 pages, 3 figures

R2 v1 2026-06-21T11:44:42.527Z