On tilings defined by discrete reflection groups

Details On tilings defined by discrete reflection groups On tilings defined by discrete reflection groups

2009-11-19

arxiv.org/abs/0911.3919v1

Mathematics

Representation Theory

8 pages, 5 figures, to appear in Izvestiya RAN

Scientific paper

The recent articles of Waldspurger and Meinrenken contained the results of tilings formed by the sets of type $(1-w)C^\circ$, $w\in W$, where $W$ is a linear or affine Weyl group, and $C^\circ$ is an open kernel of a fundamental chamber $C$ of the group $W$. In this article we generalize these results to cocompact hyperbolic reflection groups. We also give more clear and simple proofs of the Waldspurger and Meinrenken theorems.

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