In a paper I am looking at, part of a Lemma starts as follows;
Let $R$ be an irreducible root system. Suppose that $a, b \in R$ are two roots with $| b | \geq |a |$, choose $k \in \{ 1, 2, 3 \} $ to satisfy $ |b | = \sqrt{ k } | a | $. Let $ \langle a , b \rangle $ denote the root system generated by $a$ and $b$.
What is meant by $a$ and $b$ generating a root system? I am struggling to find any definition of this.