Abstract

Abstract Given such a finite linear reflection group, there is a natural and canonical way to isolate a fundamental domain in the reflection space bounded by reflecting hyperplanes. The associated diagram is then obtained by taking for nodes these hyperplanes, joining two nodes if the reflections corresponding to these hyperplanes do not commute and labelling the resulting edge by the order of the product of these two reflections. (This number is of course directly related to the angle between the roots and also the angle between the two hyperplanes.) Conversely, given a diagram, a realization by means of hyperplanes having the right angles leads to a reflection group, namely the group generated by all reflections in these hyperplanes.

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