  A family of polynomial \tau-functions for the NLS-Toda hierarchy is
constructed. The hierarchy is associated with the homogeneous vertex operator
representation of the affine algebra \g of type A_1^{(1)}. These \tau-functions
are given explicitly in terms of Schur functions that correspond to rectangular
Young diagrams. It is shown that an arbitrary polynomial \tau-function which is
an eigenvector of d, the degree operator of \g, is contained in the family. By
the construction, any \tau-function in the family becomes a Virasoro singular
vector. This consideration gives rise to a simple proof of known results on the
Fock representation of the Virasoro algebra with c=1.
