Very stable regular $G$-Higgs bundles

Abstract

We give a classification of very stable $G$-Higgs bundles in the generically regular Higgs field case for $G$ an arbitrary connected semisimple complex group. This extends the classification for $G={\mathrm{GL}}_n(\mathbb{C})$ and fixed point type $(1,1,\dots ,1)$ given by Hausel and Hitchin.

32 pages, comments are welcome