Multiplicative Higgs bundles and involutions

Abstract

In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta )$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a multiplicative Higgs bundle taking values in a symmetric variety associated to $\theta$, 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 $\theta$.

arXiv comment44 pages, 2 tables. We have included Section 2.8 about the wonderful compactification, in order to remark the relation of the Guay embedding with the Cox ring construction of Brion and give a explicit example of a Guay embedding

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