  For each Drinfeld-Sokolov integrable hierarchy associated to affine Kac-Moody
algebra, we obtain a uniform construction of tau function by using
tau-symmetric Hamiltonian densities, moreover, we represent its Virasoro
symmetries as linear/nonlinear actions on the tau function. The relations
between the tau function constructed in this paper and those defined for
particular cases of Drinfeld-Sokolov hierarchies in the literature are
clarified. We also show that, whenever the affine Kac-Moody algebra is
simply-laced or twisted, the tau functions of the Drinfeld-Sokolov hierarchy
coincide with the solutions of the corresponding Kac-Wakimoto hierarchy from
the principal vertex operator realization of the affine algebra.
