In this section, we develop the theory of Coxeter groups with a particular emphasis on the hyperbolic case.
The importance of Coxeter groups for the BKL analysis stems from the fact that in the case of the
gravitational theories that have been studied most (pure gravity, supergravities), the group generated by the
reflections in the billiard walls is a Coxeter group. This follows, in turn, from the regularity of
the corresponding billiards, whose walls intersect at angles that are integer submultiples of
.
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