  We present a pair of symmetric formulations of the matter sector of the
stationary effective action of heterotic string theory that arises after the
toroidal compactification of d dimensions. The first formulation is written in
terms of a pair of matrix potentials Z_1 and Z_2 which exhibits a clear
symmetry between them and can be used to generate new families of solutions on
the basis of either Z_1 or Z_2; the second one is an O(d+1,d+n+1)-invariant
formulation which is written in terms of a matrix vector W endowed with an
O(d+1,d+n+1)-invariant scalar product which linearizes the action of the
O(d+1,d+n+1) symmetry group on the coset space O(d+1,d+n+1)/[O(d+1)XO(d+n+1)];
this fact opens as well a simple solution--generating technique which can be
applied on the basis of known solutions. A special class of extremal solutions
is indicated by asuming a simple ansatz for the matrix vector W that reduces
the equation of motion to the Laplace equation for a real scalar function.
