Locally unitary groups and regular polytopes
refreshments at 3:45pm
Complex groups generated by involutory reflections arise naturally in the
modern theory of abstract regular polytopes. These groups preserve a
hermitian form on complex n-space and are generated by n involutory
hyperplane reflections. We are particularly interested in the case
that the subgroups generated by all but a few generating reflections
are finite (unitary) groups. For example, all the subgroups
generated by n-1 reflections may be finite.
We explain how the enumeration of certain finite universal regular
polytopes can be accomplished through the enumeration of certain
types of finite complex reflection groups, and describe all the
finite groups and their diagrams which arise in this context. This
is joint work with Peter McMullen.
Speaker's Contact Info: schulte(at-sign)research.neu.edu
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