Properties of the generalized Lax pair

The generalized Lax operator has the following properties:

- The gauge covariance. For , consider the transformation acting on the currents (33) and ghosts , as follows:Then transforms in a covariant way:
- Zero curvature:
- Covariance under the BRST transformations. When we act on the currents (33) and ghosts , by the BRST transformation:then transforms in a covariant way: