In arXiv: 1802.02833 Guichard and Wienhard introduced the notion of $\Theta $-positivity, a
generalization of Lusztig's total positivity to real Lie groups that are not necessarily split …

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures,
when G is a real reductive Lie group, and establish a correspondence between these …

We introduce a new class of sl_2-triples in a complex simple Lie algebra g, which we call
magical. Such an sl_2-triple canonically defines a real form and various decompositions of …

We consider the moduli space M (G) of G‐Higgs bundles over a compact Riemann surface
X, where G is a complex semisimple Lie group. This is a hyperkähler manifold …

Some connected components of a moduli space are mundane in the sense that they are
distinguished only by obvious topological invariants or have no special characteristics …

In this paper, we derive a maximum principle for a type of elliptic systems and apply it to
analyze the Hitchin equation for cyclic Higgs bundles. We show several domination results …

The moduli spaces for Higgs bundles associated to real Lie groups and a closed Riemann
surface have multiple connected components. This survey provides a compendium of results …

Through Cayley and Langlands type correspondences, we give a geometric description of
the moduli spaces of real orthogonal and symplectic Higgs bundles of any signature in the …

In this paper we study the-fixed points in moduli spaces of Higgs bundles over a compact
Riemann surface for a complex semisimple Lie group and its real forms. These fixed points …

Abstract Let L=(L,[⋅,⋅], δ) be an algebraic Lie algebroid over a smooth projective curve X of
genus g≥ 2 such that L is a line bundle whose degree is less than 2− 2 g. Let r and d be …