 Solution

Let $s_i=w_{{\alpha }_i}$. The root reflection formula is $s_i(\gamma )=\gamma -⟨\gamma ,{\alpha }_i^{\vee }⟩{\alpha }_i$. Applying the Cartan integers from part (b), the images of the chosen simple roots areIn particular, the two end-node Weyl reflections fix the opposite end node.