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Description: |
We study the fixed point loci on the moduli space M of GL(n,C)-Higgs bundles (over a curve) for the action of tensorization by a torsion line bundle of order n. This is a hyperholomorphic loci which can be equipped with a hyperholomorphic sheaf, hence is constitutes a BBB-brane on M. Such a brane is expected to be dual, via mirror symmetry, to a BAA-brane on M, i.e. to a complex Lagrangian subvariety equipped with a flat bundle. We find this BAA-brane and show that it can described via certain Hecke modifications. Finally we prove the duality statement via explicit Fourier-Mukai transform. It is noteworthy that these branes lie over the singular locus of the Hitchin fibration. Joint work together with E. Franco, P. Gothen and A. Peon-Nieto.
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