Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 102 / 3 / ii / Solution

The Weyl reflection formula $s_{\alpha }(x)=x-⟨x,{\alpha }^{\vee }⟩\alpha$ becomes especially concrete on $x=(x_1,\dots ,x_n)$:with all unlisted coordinates fixed. The Weyl group is therefore the group of signed permutations