Virasoro actions and harmonic maps (after Schwarz). (English) Zbl 1153.53046

Summary: 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.


53C43 Differential geometric aspects of harmonic maps
35Q58 Other completely integrable PDE (MSC2000)
17B68 Virasoro and related algebras
58E20 Harmonic maps, etc.
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