The N=2 supersymmetric unconstrined matrix GNLS hierarchies

The generalization of the N = 2 supersymmetric chiral matrix (k | n,m)-GNLS hierarchy (Lett. Math. Phys.45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N = 2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax-pair representation in terms of N = 2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N = 2 superfields, it reproduces the N = 2 chiral matrix (k | n,m)-GNLS hierarchy, while in the scalar case, k = 1, it is equivalent to the N = 2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example—the N = 2 unconstrained (1 | 1,0)-GNLS hierarchy—and its reduction to the N = 2 supersymmetric α = 1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.