Locally unitary groups and regular polytopes

Egon Schulte

Northeastern University

April 10,
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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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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