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LieTypes :: highestRoot

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

Synopsis

Description

Let R be an irreducible root system of rank m, and choose a base of simple roots Δ= {α1,...,αm}. Then there is a unique root θ such that when θ is expanded in terms of the simple roots, i.e. θ= ∑ci αi, the sum ∑ci 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 sl3, the highest root θ is ω1+ ω2, where ω1 and ω2 are the fundamental dominant weights.

i1 : highestRoot("A",2)

o1 = {1, 1}

o1 : List

Ways to use highestRoot :