Abstract
We present a conformally covariant linear system for the self-dual Yang-Mills equations. The spectral parameter is a projective twistor CP 3. A geometrical interpretation of the linear system is given. SO(4) covariant vector-currents, depending on two antisymmetric irreducible constant tensors, besides the spectral parameter, are built. SO(4) covariant Bäcklund transformations are constructed. They depend on four parameters, besides the spectral parameter and the gauge group index. One finds families of Bäcklund-transformations subalgebras, characterized by a SO(4) invariant constraint, with an embedded loop-algebra structure.
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