what The reflection σi through the hyperplane perpendicular to αi is the same as permutation of the adjacent i-th and (i + 1)-th coordinates. Such transpositions generate the full permutation group. For adjacent simple roots, σi(αi+1) = αi+1 + αi = σi+1(αi) = αi + αi+1, that is, reflection is equivalent to adding a multiple of 1; but reflection of a simple root perpendicular to a nonadjacent simple root leaves it unchanged, differing by a multiple of 0.