Multiplicative Higgs bundles and involutions

Abstract

In this paper we generalize the theory of multiplicative G-Higgs bundles over a curve to pairs (G,θ), where G is a reductive algebraic group and θ is an involution of G. This generalization involves the notion of a multiplicative Higgs bundle taking values in a symmetric variety associated to θ, or in an equivariant embedding of it. We also study how these objects appear as fixed points of involutions of the moduli space of multiplicative G-Higgs bundles, induced by the involution θ.