| Résume | Very stable Higgs bundles are a specific type of Hodge bundles within the moduli space of G-Higgs bundles. They were introduced by Hausel and Hitchin within the context of mirror symmetry, motivated by the study of Hodge bundle upward flows. These are Lagrangian subvarieties of the moduli space which can be associated to them. Given an arbitrary connected semisimple complex Lie group G, we will classify very stable G-Higgs bundles with generically regular Higgs field by relating the problem to the geometry of the affine Grassmannian of G via certain kind of Hecke transformations. This extends the work of Hausel and Hitchin for type (1, 1, ..., 1) Hodge bundles in the case of \(GL_{n}\left( \mathbb{C}\right)
\). |
