Spherical simplices generating discrete reflection groups

A. Felikson

paper

Spherical simplices generating discrete reflection groups

arXiv:math/0212244

Abstract

Let $P$ be a simplex in $S^{n}$ and $G_{P}$ be a group generated by the reflections with respect to the facets of $P$ . We are interested in the case when the group $G_{P}$ is discrete. In this case we say that $G$ generates the discrete reflection group $G_{P}$ . We develop the criteria for a simplex generating a discrete reflection group. We also describe all indecomposable spherical simplices generating discrete reflection groups.

21 pages, 3 figures, 4 tables