Torsion line bundles and branes on the Hitchin system

<p>We study the fixed loci for the action of tensorisation by a line bundle of order <em>n</em> on the moduli space of Higgs bundles for the Langlands self-dual group GL(<em>n</em>,C). We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then show how these branes are naturally dual via explicit Fourier-Mukai transform. It is noteworthy that these branes lie over the singular locus of the Hitchin fibration.</p>