Reflection subgroups of reflection groups

Author： Felikson A.   Tumarkin P.  

Publisher： Springer Publishing Company

ISSN： 0016-2663

Source： Functional Analysis and Its Applications, Vol.38, Iss.4, 2004-10, pp. : 313-314

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Abstract

Let G be a discrete group generated by reflections in hyperbolic or Euclidean space, and let H ⊂ 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.

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