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The infinite-parameter "hidden symmetry" algebra for the complex self-dual SU(N) Yang-Mills fields is extended from SL(N, C)C[λ] to SL(N, C)C[λ, λ^-1]SL(N, C). Furthermore, we also find an infinite set of infinitesimal "hidden symmetry" transformations, indexed by all integers, which can maintain the reality of the self-dual Yang-Mills potentials. Their infinite-parameter Lie algebra is shown to be related to an infinitedimensional symmetric space with isotropy group SU(N)R[λ].
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Chau et al. (1982) studied this question.
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