Tilings defined by affine Weyl groups

Eckhard Meinrenken

Vol. 242 (2009), No. 2, 333–343

DOI: 10.2140/pjm.2009.242.333

Abstract

Let W be a Weyl group, presented as a reflection group on a Euclidean vector space V , and C ⊂ V an open Weyl chamber. In a recent paper, Waldspurger proved that the images (id−w)(C) for w ∈ W are all disjoint, with union the closed cone spanned by the positive roots. We prove that similarly, the images (id−w)(A) of the open Weyl alcove A, for w ∈ W^aff in the affine Weyl group, are disjoint and their union is V .

Keywords

affine Weyl group, reflection groups, alcoves

Mathematical Subject Classification 2000

Primary: 20F55, 22E46

Milestones

Received: 12 January 2009

Revised: 4 February 2009

Accepted: 6 February 2009

Published: 1 October 2009