Let $\mathfrak{g}$ be a finite-dimensional complex semisimple Lie algebra, let $\mathfrak{h} \subset \mathfrak{g}$ be a Cartan subalgebra, and let $\Phi \subset \mathfrak{h}^*$ be the corresponding root system. For each root $\alpha \in \Phi$, let $\alpha^\vee$ denote the coroot of $\alpha$, and define the reflection