Question 2: What is a plain English and highschool level linear algebra recipe to finding the roots and weights given su(2) generators?

Question

You are given the generators of su(2).

You want to get the roots and weights.

What are the steps?

Using plain English. To me, the idea looks as such

• Write the Cartan generators

• Find the eigenvalues

• These are the root

• Weights have something to do with the normalized eigenvectors corresponding to the roots

How close? How is it done in plain English and high school-level math