English

Commuting elements in reductive groups and Higgs bundles on abelian varieties

Algebraic Geometry 2021-05-25 v1

Abstract

Let G be a connected real reductive algebraic group, and let K be a maximal compact subgroup of G. We prove that the conjugation orbit space Hom(Z^{2d},K)/K is a strong deformation retract of the space Hom(Z^{2d},G)/G of equivalence classes of representations of Z^{2d} into G. This is proved by showing that the homotopy type of the moduli space of principal G-Higgs bundles of vanishing rational characteristic classes on a complex abelian variety of dimension d depends only on K.

Keywords

Cite

@article{arxiv.1305.3429,
  title  = {Commuting elements in reductive groups and Higgs bundles on abelian varieties},
  author = {Indranil Biswas and Carlos Florentino},
  journal= {arXiv preprint arXiv:1305.3429},
  year   = {2021}
}
R2 v1 2026-06-22T00:16:51.499Z