Projects and Assignments in Pure Mathematics
Infinite reflection groups
Finite reflection groups are treated, for example, in
J E Humphreys, "Reflection groups and Coxeter groups" (Cambridge).
Affine reflection groups on finite spaces (which are infinite groups)
are also treated there, but the geometry of polytopes defined by
reflection walls starts to get quite interesting, and more can be said
than Humphreys finds room for in his book.
In the project one would develop an understanding of the construction of
these groups (or a subset of them), and study the combinatorics of the
Some level 1 group theory and level 2 linear algebra.
Ideally also a level 3 module on groups and symmetry.
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