he Coxeter Plane is obtained from the root system (of a Lie algebra) by projecting the roots to a certain 2-dimensional plane. The resulting picture was discovered by Coxeter in his investigations of polytopes - but rarely appears in the Lie theory literature. We shall give another description of the Coxeter Plane, arising (in a rather unexpected way) from the theory of ordinary differential equations and integrable systems. This is joint work with Nan-Kuo Ho of National Tsing-Hua University, Taiwan.

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