Let R be an irreducible root system of rank m, and choose a base of simple roots Δ= {α_{1},...,α_{m}}. Then there is a unique root θ such that when θ is expanded in terms of the simple roots, i.e. θ= ∑c_{i} α_{i}, the 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 θ is ω_{1}+ ω_{2}, where ω_{1} and ω_{2} are the fundamental dominant weights.
i1 : highestRoot("A",2) o1 = {1, 1} o1 : List |