Guillermo Gallego: Multiplicative Hitchin fibrations and Langlands duality
Abstract: Hitchin fibrations for Langlands dual groups, when restricted to a dense open locus of the Hitchin base, are known to be dual (relative) Beilinson 1-motives; that is, the neutral connected components of their coarse moduli spaces are dual abelian schemes and their inertia and component groups are exchanged under Cartier duality. Following the recent preprint (arxiv:2509.14364), we explore a similar situation in the context of multiplicative Hitchin fibrations. These are group-valued analogues of the Hitchin fibration, modelled over the Steinberg map from a reductive group to the GIT quotient of it by its own adjoint action. The corresponding pairs matched under duality can be classified in terms of the duality for affine Dynkin diagrams. In this talk, we will provide a self-contained introduction to multiplicative Hitchin fibrations (untwisted and twisted) as well as an explanation of this duality.