Coset approach to the N=2 supersymmetric matrix GNLS hierarchies

We discuss a large class of coset constructions of the N=2 sl(n|n− 1) affine superalgebra. We select admissible subalgebras, i.e. subalgebras that induce linear chiral/antichiral constraints on the coset supercurrents. We show that all the corresponding coset constructions lead to N=2 matrix GNLS hierarchies. We develop an algorithm to compute the relative Hamiltonians and flows. We spell out completely the case of the N=2 ŝl(3|2), which possesses four admissible subalgebras. The non–local second Hamiltonian structure of the N=2 matrix GNLS hierarchies is obtained via Dirac procedure from the local N=2 sl(n|n − 1) affine superalgebra. We observe that to any second Hamiltonian structure with pure bosonic or pure fermionic superfield content there correspond two different N=2 matrix GNLS hierarchies. E-Mail: 1) [email protected] 2) [email protected] 3) [email protected]