Higgs bundles over elliptic curves for real groups
  We study topologically trivial $G$-Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space, the associated Hitchin fibration and the finite morphism to the moduli space of $G^{\mathbb{C}}$-Higgs bundles. 
Emilio Franco, \'Oscar Garc\'ia-Prada, P.E. Newstead
math.AG