FACTORIZATIONS FOR SELF-DUAL GAUGE-FIELDS

For a particular class of patching matrices on P3(ℂ), including those for the complex instanton bundles with structure group Sp(k,ℂ) or O(2k,ℂ), we show that the associated Riemann-Hilbert problem G(x, λ)=G-(x, λ)·G+-1(x, λ) can be generically solved in the factored form G-=φ1φ2..... φn. If G{cyrillic}=G{cyrillic}n is the potential generated in the usual way from G-, and we set ψi=φ1....., φi with ψn=G-, then each ψialso generates a selfdual gauge potential Γi. The potentials are connected via the "dressing transformations" {Mathematical expression} of Zakharov-Shabat. The factorization is not unique; it depends on the (arbitrary) ordering of the poles of the patching matrix. © 1990 Springer-Verlag.