Non-local conservation laws and flow equations for supersymmetric integrable hierarchies

An infinite series of Grassmann-odd and Grassmann-even Row equations is def ined for a class of supersymmetric integrable hierarchies associated with l oop superalgebras. All these Rows commute with the mutually commuting boson ic ones originally considered to define these hierarchies and, hence, provi de extra fermionic and bosonic symmetries that include the built-in N = 1 s upersymmetry transformation. The corresponding non-local conserved quantiti es are also constructed. As an example, the particular case of the principa l supersymmetric hierarchies associated with the affine superalgebras with a fermionic simple root system is discussed in detail.