Instantons on hyperkaehler manifolds allow a number of equivalent descriptions:
a) via the Hitchin-Kobaiashi correspondence, as stable holomorphic bundles over the underlying variety or
b) as holomorphic bundles over its twistor space (with certain triviality conditions).
For the case of instantons on multi-Taub-NUT we use either descriptions to provide a finite monad construction of the respective bundles.
A nonlinear version of the Fourier transform, generalizing the ADHM-Nahm transform, for such instantons leads to data satisfying and ODE. This data is organized in a bow, which is a natural generalization of a quiver. We use the bow description to reproduce exactly the monad above. This proves the completeness of the bow construction of instantons.
These results are obtained in collaboration with Jacques Hurtubise.
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