Thursday, January 31, 2013

Coxeter planes

Here are a few nice Coxeter projections of representations of finite Lie algebras. If you don't know what a Coxeter projection is, or a finite Lie algebra for that matter, have a look at my PhD thesis (from which I took these pictures). Or, visit John Stembridge's website for more information and pictures.

Update: some of these pictures do not show the full representation, but only a subset.


The orbits of the two highest dominant weights of the 1764 representation of A5.

The orbits of the two highest dominant weights of the 5985 representation of A17.

The orbits of the two highest dominant weights of the 442 representation of B6.

The adjoint representation of B19.

The adjoint representation of D10.