Tilings defined by affine Weyl groups

Details Tilings defined by affine Weyl groups Tilings defined by affine Weyl groups

2008-11-24

arxiv.org/abs/0811.3880v2

Pacific J. Math. 242 (2009), no. 2, 333-343

Mathematics

Group Theory

9 pages, 3 figures

Scientific paper

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.

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