This article is cited in 5 papers

Brief communications

Reflection Subgroups of Reflection Groups

P. V. Tumarkin, A. A. Felikson

Independent University of Moscow

Abstract: Let $G$ be a discrete group generated by reflections in hyperbolic or Euclidean space, and let $H\subset G$ be a finite index reflection subgroup. Suppose that the fundamental chamber of $G$ is a finite volume polytope with $k$ facets. We prove that the fundamental chamber of $H$ has at least $k$ facets.

Keywords: reflection group, Coxeter polytope.

UDC: 512.817.72+514.174.5

Received: 31.03.2003

DOI: 10.4213/faa131

 English version: Functional Analysis and Its Applications, 2004, 38:4, 313–314

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