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Orthogonal groups in characteristic 2 acting on polytopes of high rank

Banff International Research Station for Mathematical Innovation and Discovery

In a series of three papers, Monson and Schulte showed that, subject to some mild constraints, certain families of real reflection groups can be reduced modulo odd primes to yield finite string C-subgroups of orthogonal groups. Further, polytopes of any desired rank can be constructed this way. In this talk I will show that the latter is also true for orthogonal groups defined over any non-prime field of characteristic 2. Of course, the modular reduction method cannot be used for such groups, so the polytopes are constructed from scratch using analogues of reflections. This is a report on recent joint work with J.T. Ferrara and Dimitri Leemans.

Mathematics; Convex and discrete geometry; Group theory and generalizations; Discrete mathematics

video/mp4

Author affiliation: Bucknell University

2018-03-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64890

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/