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LieTypes :: highestRoot

highestRoot -- returns the highest root of a simple Lie algebra



Let R be an irreducible root system of rank m, and choose a base of simple roots $\Delta = \{\alpha_1,...,\alpha_m\}$. Then there is a unique root $\theta$ such that when $\theta$ is expanded in terms of the simple roots, i.e. $\theta= \sum c_i \alpha_i$, the sum $\sum c_i$ is maximized. The formulas implemented here are taken from the tables following Bourbaki's Lie Groups and Lie Algebras Chapter 6.

In the example below, we see that for $sl_3$, the highest root $\theta$ is $\omega_1+ \omega_2$, where $\omega_1$ and $\omega_2$ are the fundamental dominant weights.

i1 : highestRoot("A",2)

o1 = {1, 1}

o1 : List

Ways to use highestRoot :

For the programmer

The object highestRoot is a method function.