Lorentz invariance of the pure spinor BRST cohomology for the superstring

In a previous Letter, the BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green–Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this Letter, the SO(9,1) Lorentz generators are explicitly constructed using this SO(8) parameterization, proving the Lorentz invariance of the pure spinor BRST cohomology.