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. subalgebr as that induce linear chiral/antichiral constraints on the coset super currents. We show that all the corresponding coset constructions lead to N = 2 matrix GNLS hierarchies. We develop an algorithm to compute t he relative Hamiltonians and flows. We spell out completely the case o f the N = 2 <(sl)over cap>(3\2), which possesses four admissible subal gebras, The non-local second Hamiltonian structure of the N = 2 matrix GNLS hierarchies is obtained via the Dirac procedure from the local N = 2 sl(n\n-1) affine superalgebra. We observe that to any second Hami ltonian structure with pure bosonic or pure fermionic superfield conte nt there correspond two different N = 2 matrix GNLS hierarchies. (C) 1 998 Elsevier Science B.V.