Action of a simple reflection on positive roots
= Action of a simple reflection on positive roots
For a simple root $\alpha$, the reflection $s_\alpha$ sends $\alpha$ to $-\alpha$ and permutes all other positive roots.
= Action of a simple reflection on positive roots
For a simple root $\alpha$, the reflection $s_\alpha$ sends $\alpha$ to $-\alpha$ and permutes all other positive roots.