Kac-Moody algebra in the self-dual Yang-Mills equation

In the $J$ formulation of self-dual Yang-Mills equations, we propose a parametric infinitesimal transformation, which generates new solutions from any old ones and satisfies the equations of the Bianchi-Bäcklund transformation with parameter. Expanding in the parameter, we obtain an infinite number of transformations, all of which leave the self-dual Yang-Mills equation invariant. We discuss the group properties for these transformations, and find that they form a Lie group, to which the Lie algebra is an infinite-dimensional Kac-Moody algebra, a mathematical structure encountered in the recent development of principal chiral theories.