The parabolic transformations show up as x + → → x + , x − − → → x − − + δ δ i j α α i x j + α α 2 2 x + , x i → → x i + α α i x + . Another set of parabolic transformations show up as x + → → x + + δ δ i j α α i x j + α α 2 2 x − − , x − − → → x − − and x i → → x i + α α i x − − .