Definition
Let E be a finite-dimensional Euclidean space. A finite reflection group is a subgroup of the general linear group of E which is generated by a set of orthogonal reflections across hyperplanes passing through the origin. An affine reflection group is a discrete subgroup of the affine group of E that is generated by a set of affine reflections of E (without the requirement that the reflection hyperplanes pass through the origin).
The corresponding notions can be defined over other fields, leading to complex reflection groups and analogues of reflection groups over a finite field.
Read more about this topic: Reflection Group
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