  The actions of a half Virasoro algebra have appeared in many integrable
systems. In this paper we show that there is an action of a (Half) Virasoro
algebra on the space of (2+0) harmonic maps into a Lie group. This action is
generated by a natural action on the frames. A similar calculation on the
space-time (1+1) harmonic maps yields formulas generated by John Schwarz.
