Multiplicative Higgs bundles, monopoles and involutions

Guillermo Gallego, Universidad Complutense de Madrid

Multiplicative Higgs bundles are a natural analogue of Higgs bundles on Riemann surfaces, where the Higgs field now takes values on the adjoint group bundle, instead of the adjoint Lie algebra bundle. In the work of Charbonneau and Hurtubise, they have been related to singular monopoles over the product of a circle with the Riemann surface.

In this talk we study the natural action of an involution of the group on the moduli space of multiplicative Higgs bundles, also from the point of view of monopoles. This provides a "multiplicative analogue" of the theory of Higgs bundles for real groups.

MC 5403