The Discrete Symmetries of the N=2 Supersymmetric GNLS Hierarchies

The discrete symmetry transformations of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed. Their bosonic limit is analyzed and new discrete symmetries of the modified GNLS hierarchy are derived. The explicit relations connecting the integrable hierarchy, produced by the junction of the Lax operators for the N=2 supersymmetric a=4 KdV and (n-1,m)-GNLS hierarchies, to the N=2 supersymmetric (n,m)-GNLS hierarchy are established.