A SIMPLE EXAMPLE OF MODULAR-FORMS AS TAU-FUNCTIONS FOR INTEGRABLE EQUATIONS

We show how classical modular forms and functions appear as tau-functi ons for a certain integrable reduction of the self-dual Yang-Mills equ ations obtained by S. Chakravarty, M. Ablowitz, and P. Clarkson [6]. W e discuss possible consequences of this novel phenomenon in integrable systems which indicate deep connections between integrable equations, group representations, modular forms, and moduli spaces.