Let R be an irreducible root system of rank m, and choose a base of simple roots Δ= {α1,...,αm}. This function returns all the roots that are nonnegative linear combinations of the simple roots. 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 positive roots are α1, α2, and α1+α2.
i1 : sl3=simpleLieAlgebra("A",2) o1 = sl3 o1 : LieAlgebra |
i2 : positiveRoots(sl3) o2 = {{2, -1}, {1, 1}, {-1, 2}} o2 : List |