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arXiv · 1011.6421

Cyclic Higgs bundles and the affine Toda equations

David Baraglia
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Abstract

We introduce a class of Higgs bundles called cyclic which lie in the Hitchin component of representations of a compact Riemann surface into the split real form of a simple Lie group. We then prove that such a Higgs bundle is equivalent to a certain class of solutions to the affine Toda equations. We further explain this relationships in terms of lifts of harmonic maps.

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David Baraglia. 2010-11-30. Cyclic Higgs bundles and the affine Toda equations. https://doi.org/10.1007/s10711-014-0003-2

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